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  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_cde25ae6-2f1e-4b45-a30b-92b8e3f1f535_negatedLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: accumulated amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_c35d53c8-8d04-4107-b990-a93c648acbad_verboseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PercentageCalculationBaseByCategoryDomain_7ee06ea5-7132-4f57-b2fe-a5af7dab8d2c_terseLabel_en-US" xlink:label="lab_hgit_PercentageCalculationBaseByCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Domain]</link:label>
    <link:label id="lab_hgit_PercentageCalculationBaseByCategoryDomain_label_en-US" xlink:label="lab_hgit_PercentageCalculationBaseByCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Domain]</link:label>
    <link:label id="lab_hgit_PercentageCalculationBaseByCategoryDomain_documentation_en-US" xlink:label="lab_hgit_PercentageCalculationBaseByCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PercentageCalculationBaseByCategoryDomain" xlink:href="hgit-20250930.xsd#hgit_PercentageCalculationBaseByCategoryDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PercentageCalculationBaseByCategoryDomain" xlink:to="lab_hgit_PercentageCalculationBaseByCategoryDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_304bd975-b0b3-426a-8b78-34de131bb087_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_3a10b05c-b39d-4562-8246-509c96368950_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in Real Estate-Related Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentPolicyTextBlock" xlink:to="lab_us-gaap_InvestmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_3170ecdc-124f-4b2c-9410-f6fc724ae6f8_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DividendsIncurredButNotYetPaid_c0cb70ea-4851-4ca3-8d49-31e5f7a60bd2_verboseLabel_en-US" xlink:label="lab_hgit_DividendsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Distributions declared and unpaid</link:label>
    <link:label id="lab_hgit_DividendsIncurredButNotYetPaid_label_en-US" xlink:label="lab_hgit_DividendsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Incurred But Not Yet Paid</link:label>
    <link:label id="lab_hgit_DividendsIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_hgit_DividendsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividends Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DividendsIncurredButNotYetPaid" xlink:href="hgit-20250930.xsd#hgit_DividendsIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DividendsIncurredButNotYetPaid" xlink:to="lab_hgit_DividendsIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_8ab38ba2-4ba9-431a-a45b-2bee4487e5ce_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_0fed58c4-6d37-437f-a814-d32c2f6b8893_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_18d4ee37-adef-4734-82d2-003ca367e140_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_5e11c613-f937-4688-9dac-e9658ea0ae65_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_b21f3f0c-02ba-4d45-9a1d-1a9c18bf591e_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IPOMember_fb888993-5ee6-4436-98c3-e084fc9cd788_terseLabel_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IPO</link:label>
    <link:label id="lab_us-gaap_IPOMember_label_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IPO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IPOMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IPOMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IPOMember" xlink:to="lab_us-gaap_IPOMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_4a67adc8-6b75-4e51-a415-7a07e9bce0bb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Financing Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfFinancingCosts" xlink:to="lab_us-gaap_PaymentsOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_424ce9b3-48a1-4d6d-9e9f-e4ebff4a5e1e_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable to Banks [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableToBanksMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableToBanksMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableToBanksMember" xlink:to="lab_us-gaap_NotesPayableToBanksMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_eb65a4da-612c-475b-988d-5364afcdfd52_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_1a5c738a-7d36-4de8-9cc8-9289722b7f50_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_d1d62f42-1327-4ae9-b473-8a8c8d689fce_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsLeasingNet_1fdea26d-e6a2-4c8c-a8e8-b02511035112_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred leasing costs, net</link:label>
    <link:label id="lab_us-gaap_DeferredCostsLeasingNet_label_en-US" xlink:label="lab_us-gaap_DeferredCostsLeasingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Leasing, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsLeasingNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredCostsLeasingNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsLeasingNet" xlink:to="lab_us-gaap_DeferredCostsLeasingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsStock_981298bd-8a6f-4da8-8dce-8c31185409c7_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions Reinvested</link:label>
    <link:label id="lab_us-gaap_DividendsStock_label_en-US" xlink:label="lab_us-gaap_DividendsStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsStock" xlink:to="lab_us-gaap_DividendsStock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NotesPayableVariableRateMember_9ad69ad7-9475-471c-8d60-78866238ec40_terseLabel_en-US" xlink:label="lab_hgit_NotesPayableVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate Loans</link:label>
    <link:label id="lab_hgit_NotesPayableVariableRateMember_label_en-US" xlink:label="lab_hgit_NotesPayableVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Variable Rate [Member]</link:label>
    <link:label id="lab_hgit_NotesPayableVariableRateMember_documentation_en-US" xlink:label="lab_hgit_NotesPayableVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Payable, Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NotesPayableVariableRateMember" xlink:href="hgit-20250930.xsd#hgit_NotesPayableVariableRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NotesPayableVariableRateMember" xlink:to="lab_hgit_NotesPayableVariableRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PercentageOfPortfolioLeased_e68ce27c-5f94-41bb-98b6-030a28504029_terseLabel_en-US" xlink:label="lab_hgit_PercentageOfPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portfolio leased (in percent)</link:label>
    <link:label id="lab_hgit_PercentageOfPortfolioLeased_label_en-US" xlink:label="lab_hgit_PercentageOfPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Portfolio Leased</link:label>
    <link:label id="lab_hgit_PercentageOfPortfolioLeased_documentation_en-US" xlink:label="lab_hgit_PercentageOfPortfolioLeased" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage of Portfolio Leased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PercentageOfPortfolioLeased" xlink:href="hgit-20250930.xsd#hgit_PercentageOfPortfolioLeased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PercentageOfPortfolioLeased" xlink:to="lab_hgit_PercentageOfPortfolioLeased" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_050409c9-9170-4e20-a890-0930206bfcca_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic income (loss) per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_218a75a2-e90a-4fb0-bc1e-c7f00d23a403_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">RELATED PARTY TRANSACTIONS</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_484d20d6-86e9-4d4a-8bd2-935df30f8578_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change in accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RunwayLivingMember_05f5a8f0-07d6-4551-b85c-6ef6064b7703_terseLabel_en-US" xlink:label="lab_hgit_RunwayLivingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Runway - Living</link:label>
    <link:label id="lab_hgit_RunwayLivingMember_label_en-US" xlink:label="lab_hgit_RunwayLivingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Runway - Living [Member]</link:label>
    <link:label id="lab_hgit_RunwayLivingMember_documentation_en-US" xlink:label="lab_hgit_RunwayLivingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Runway - Living</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RunwayLivingMember" xlink:href="hgit-20250930.xsd#hgit_RunwayLivingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RunwayLivingMember" xlink:to="lab_hgit_RunwayLivingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassDMember_7992ce98-959c-40f9-834b-5f4b298dd4dc_terseLabel_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class D</link:label>
    <link:label id="lab_hgit_CommonClassDMember_label_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class D [Member]</link:label>
    <link:label id="lab_hgit_CommonClassDMember_documentation_en-US" xlink:label="lab_hgit_CommonClassDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class D [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassDMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassDMember" xlink:to="lab_hgit_CommonClassDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_7064a9d8-5c5a-4d26-b817-978ec956ef40_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock by Subsidiary or Equity Investee [Table]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_6f700d74-0cee-47f0-907a-3d66efc4bc15_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_898fe826-7b78-4641-b6d9-a4a4cb7ad110_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PercentageCalculationBasebyCategoryAxis_3d1120f8-4b7e-49f7-9890-017f1c092ae6_terseLabel_en-US" xlink:label="lab_hgit_PercentageCalculationBasebyCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Axis]</link:label>
    <link:label id="lab_hgit_PercentageCalculationBasebyCategoryAxis_label_en-US" xlink:label="lab_hgit_PercentageCalculationBasebyCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Axis]</link:label>
    <link:label id="lab_hgit_PercentageCalculationBasebyCategoryAxis_documentation_en-US" xlink:label="lab_hgit_PercentageCalculationBasebyCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage Calculation Base, by Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PercentageCalculationBasebyCategoryAxis" xlink:href="hgit-20250930.xsd#hgit_PercentageCalculationBasebyCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PercentageCalculationBasebyCategoryAxis" xlink:to="lab_hgit_PercentageCalculationBasebyCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AreaOfRealEstateProperty_9388e047-0493-47d7-9f99-e9cca7dca9fb_terseLabel_en-US" xlink:label="lab_us-gaap_AreaOfRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Area of real estate property (square feet)</link:label>
    <link:label id="lab_us-gaap_AreaOfRealEstateProperty_label_en-US" xlink:label="lab_us-gaap_AreaOfRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Area of Real Estate Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AreaOfRealEstateProperty" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AreaOfRealEstateProperty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AreaOfRealEstateProperty" xlink:to="lab_us-gaap_AreaOfRealEstateProperty" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_b0ed3b29-39e9-453a-b618-30cd48bf8e7e_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk (percent)</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_53480051-90b8-4eac-aa19-588dabf9a64c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember_0ca98b65-b7f6-406f-a58e-fc1156574e26_terseLabel_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Central European industrial properties, placed into service</link:label>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember_label_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Central European Industrial Properties, Placed Into Service [Member]</link:label>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember_documentation_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Central European Industrial Properties, Placed Into Service</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:href="hgit-20250930.xsd#hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:to="lab_hgit_CentralEuropeanIndustrialPropertiesPlacedIntoServiceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_537ab247-34f8-40d4-a78b-3a484910964d_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization_e2682b8c-58f5-439b-b22c-3cc354dcf991_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: accumulated amortization</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:to="lab_us-gaap_BelowMarketLeaseAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidTaxes_f1baae09-87cc-4f57-a7bb-f2e06eacd8eb_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid property taxes</link:label>
    <link:label id="lab_us-gaap_PrepaidTaxes_label_en-US" xlink:label="lab_us-gaap_PrepaidTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Taxes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidTaxes" xlink:to="lab_us-gaap_PrepaidTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesMember_4b24a862-6a1d-4683-9a5a-c7afcaa83adb_terseLabel_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Central European industrial properties</link:label>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesMember_label_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Central European Industrial Properties [Member]</link:label>
    <link:label id="lab_hgit_CentralEuropeanIndustrialPropertiesMember_documentation_en-US" xlink:label="lab_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Central European Industrial Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:href="hgit-20250930.xsd#hgit_CentralEuropeanIndustrialPropertiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:to="lab_hgit_CentralEuropeanIndustrialPropertiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_dee46ce7-c3f7-4e3f-878d-c87e329e2686_terseLabel_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense Reimbursement</link:label>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_label_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expense Reimbursements [Member]</link:label>
    <link:label id="lab_hgit_ExpenseReimbursementsMember_documentation_en-US" xlink:label="lab_hgit_ExpenseReimbursementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expense Reimbursements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ExpenseReimbursementsMember" xlink:href="hgit-20250930.xsd#hgit_ExpenseReimbursementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ExpenseReimbursementsMember" xlink:to="lab_hgit_ExpenseReimbursementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_72fdcb28-cd9a-4bbc-aa61-193a03f3ab04_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Distributions</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_1ac0d4fa-78c3-407d-9225-53d45ab5790b_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_d3d5c9a8-c1f7-488e-964a-525d1dad61e3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value By Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_a4fd7955-549c-4b6f-b875-d538efe327ba_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_e8ec807c-130c-4ed7-adb5-cc60eb70ab0e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_3cb7a000-baf2-41c6-a42d-b32c5ac4163e_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_6a6f0fe0-ba2a-4540-aaa1-8b3c597ea10e_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable, fair value</link:label>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:to="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PaymentsOnFinancingObligations_cded5947-d42b-44e7-adef-9388374db5ca_negatedTerseLabel_en-US" xlink:label="lab_hgit_PaymentsOnFinancingObligations" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on financing obligations</link:label>
    <link:label id="lab_hgit_PaymentsOnFinancingObligations_label_en-US" xlink:label="lab_hgit_PaymentsOnFinancingObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments on Financing Obligations</link:label>
    <link:label id="lab_hgit_PaymentsOnFinancingObligations_documentation_en-US" xlink:label="lab_hgit_PaymentsOnFinancingObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments on Financing Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PaymentsOnFinancingObligations" xlink:href="hgit-20250930.xsd#hgit_PaymentsOnFinancingObligations"/>
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    <link:label id="lab_hgit_ClayTerraceMember_b71b4724-8125-4481-ab92-5621f8160f77_terseLabel_en-US" xlink:label="lab_hgit_ClayTerraceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Clay Terrace</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_e6a64ff5-eae6-4c85-94f3-0f66934e5dfd_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares (in shares)</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_521eec31-af9e-45b8-969e-28f8f3e31e27_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_adf0e139-31bd-4e42-9904-7f3741f5ed7b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_53ec4ddf-81a6-4c82-a32d-58e92d5618c8_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_d32e3d63-4d3b-4f2c-b253-beb470c263ee_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND EQUITY</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
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    <link:label id="lab_dei_CoverAbstract_658719bf-5d99-4887-9bdc-4933b231796a_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
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    <link:label id="lab_srt_MaximumMember_f44f6dcf-c427-4ff8-b1f9-95ba527ae3aa_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract_53373beb-1ae3-493a-aeff-bdaa5b2ebe34_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyNetAbstract"/>
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    <link:label id="lab_hgit_CommonClassIMember_f8039887-2687-4113-9067-b93b19796b6f_terseLabel_en-US" xlink:label="lab_hgit_CommonClassIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class I</link:label>
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    <link:label id="lab_hgit_CommonClassIMember_documentation_en-US" xlink:label="lab_hgit_CommonClassIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class I [Member]</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_bd854a20-0573-4729-aed8-e416c1f3e25d_negatedLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net (income) loss attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_7b480360-78ae-4be8-a7d6-ec321da7d2ba_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_1035e573-81f3-4a8d-9dc9-02c27c6f029c_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible lease assets, net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_2deabb05-25f2-4dcf-aa24-25804c369a8a_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_4fc697a8-b8a5-4681-ac08-aaa84b6b3538_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operating Lease, Liability, to be Paid, Maturity</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
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    <link:label id="lab_us-gaap_DebtInstrumentLineItems_f10e8d93-94d0-49e0-9e17-6ad0f7a1ac6f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNetAbstract_38ce3e74-482b-40c8-a2c8-7666d1a25fef_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNetAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNetAbstract" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_571fe7a8-b4c3-4474-81df-331449f7d797_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_0ab4b253-0c44-4ffa-90ad-e784457d9c31_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ground Lease Liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassJXMember_4cd53e3e-bcaa-4a6a-8436-c0e710bb7de2_terseLabel_en-US" xlink:label="lab_hgit_CommonClassJXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class JX</link:label>
    <link:label id="lab_hgit_CommonClassJXMember_label_en-US" xlink:label="lab_hgit_CommonClassJXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class JX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassJXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassJXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class JX [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassJXMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassJXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassJXMember" xlink:to="lab_hgit_CommonClassJXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_TenantAndOtherReceivables_92e4e2b2-3a32-47c8-b7b4-456678419740_terseLabel_en-US" xlink:label="lab_hgit_TenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tenant and other receivables, net</link:label>
    <link:label id="lab_hgit_TenantAndOtherReceivables_label_en-US" xlink:label="lab_hgit_TenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tenant And Other Receivables</link:label>
    <link:label id="lab_hgit_TenantAndOtherReceivables_documentation_en-US" xlink:label="lab_hgit_TenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tenant and other receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_TenantAndOtherReceivables" xlink:href="hgit-20250930.xsd#hgit_TenantAndOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_TenantAndOtherReceivables" xlink:to="lab_hgit_TenantAndOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_e11378ca-0d78-4cdc-a5bc-2be08e6f19a2_totalLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_StatutoryTrustProgramAbstract_label_en-US" xlink:label="lab_hgit_StatutoryTrustProgramAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Trust Program [Abstract]</link:label>
    <link:label id="lab_hgit_StatutoryTrustProgramAbstract_documentation_en-US" xlink:label="lab_hgit_StatutoryTrustProgramAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Statutory Trust Progra</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_StatutoryTrustProgramAbstract" xlink:href="hgit-20250930.xsd#hgit_StatutoryTrustProgramAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_StatutoryTrustProgramAbstract" xlink:to="lab_hgit_StatutoryTrustProgramAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_2f269832-5ec7-4396-af43-ed89c20d2705_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_0e533cb3-b948-4b41-b56c-886b8f2669c4_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_dd6d356a-4981-4b91-a8ac-6effd105df5c_verboseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_0790dbcd-9efa-4268-8829-e3057b7fd7ee_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of financing lease assets</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_dec4ac82-2551-4012-a664-c28d583ce982_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before benefit (provision) for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_aaa0e9bb-2e81-49a1-9629-055ead8c31e8_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock_f9e9d7d9-a458-42df-9927-31c5681e9f6f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Assets by Geographical Location</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Revenue from External Customers and Long-Lived Assets, by Geographical Areas [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsByGeographicalAreasTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRedeemedOrCalledDuringPeriodShares_f386f291-a7b3-4976-918a-11c93395e77b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemption of common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRedeemedOrCalledDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Redeemed or Called During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRedeemedOrCalledDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:to="lab_us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_360d3130-b507-4d68-b3ce-662101287e20_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_4616a0c4-3fe0-46b2-8bca-cf8bc5554925_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_9d7e1648-fcfe-496a-85ff-91fae67eb58c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_d2f80c58-e624-4ea9-bd66-d5939606a906_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow Supplemental Disclosures</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DelawareStatutoryTrustPropertyMember_67436b09-e121-4ba1-8ec4-5361d1ae1b0d_terseLabel_en-US" xlink:label="lab_hgit_DelawareStatutoryTrustPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST Property</link:label>
    <link:label id="lab_hgit_DelawareStatutoryTrustPropertyMember_label_en-US" xlink:label="lab_hgit_DelawareStatutoryTrustPropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Delaware Statutory Trust Property [Member]</link:label>
    <link:label id="lab_hgit_DelawareStatutoryTrustPropertyMember_documentation_en-US" xlink:label="lab_hgit_DelawareStatutoryTrustPropertyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Delaware Statutory Trust Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DelawareStatutoryTrustPropertyMember" xlink:href="hgit-20250930.xsd#hgit_DelawareStatutoryTrustPropertyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DelawareStatutoryTrustPropertyMember" xlink:to="lab_hgit_DelawareStatutoryTrustPropertyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_50853d34-bbbf-47d9-bab7-641662953750_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_cb14756f-1ca2-44a1-ae89-5b0c9f82018c_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_1a219214-0844-48b5-bca2-10e42939135d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (income) loss attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_dc61d160-9c07-4bb8-a2ca-072e2dd0f832_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1_1872df3a-9456-4441-816c-ab57dee521f8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Non-cash net liabilities (assets) assumed</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Net Nonmonetary Assets Acquired (Liabilities Assumed)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1" xlink:to="lab_us-gaap_NoncashOrPartNoncashAcquisitionNetNonmonetaryAssetsAcquiredLiabilitiesAssumed1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RetailInvestmentsMember_9137b0b7-262f-490b-91df-bef0ea5f0fe5_terseLabel_en-US" xlink:label="lab_hgit_RetailInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retail investments</link:label>
    <link:label id="lab_hgit_RetailInvestmentsMember_label_en-US" xlink:label="lab_hgit_RetailInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retail Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RetailInvestmentsMember" xlink:href="hgit-20250930.xsd#hgit_RetailInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RetailInvestmentsMember" xlink:to="lab_hgit_RetailInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseInterestExpense_b03119e2-d5dc-4f9a-a8c0-ab9fc3bbdb0b_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseInterestExpense_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseInterestExpense" xlink:to="lab_us-gaap_FinanceLeaseInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_c59a51fe-a763-4ab3-a626-83d1120a41e7_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_765f7dd8-75dc-4248-84cd-d3fde632838c_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LesseeFinanceLeaseNumberOfAgreements_2143eb47-e45b-4a2b-a425-eb63b5865e64_terseLabel_en-US" xlink:label="lab_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of agreements accounted for as financing leases</link:label>
    <link:label id="lab_hgit_LesseeFinanceLeaseNumberOfAgreements_label_en-US" xlink:label="lab_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Lease, Number Of Agreements</link:label>
    <link:label id="lab_hgit_LesseeFinanceLeaseNumberOfAgreements_documentation_en-US" xlink:label="lab_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Finance Lease, Number Of Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:href="hgit-20250930.xsd#hgit_LesseeFinanceLeaseNumberOfAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:to="lab_hgit_LesseeFinanceLeaseNumberOfAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_0510f869-5b47-4e6f-b23a-50343a08e384_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tenant and Other Receivables</link:label>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivablesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:to="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_cbd70702-2fb6-465a-8945-bf1003b63486_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Distributions</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDividendsPayableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredLeasingFees_c7701f0b-f860-4999-9e87-45b0b6034ee1_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredLeasingFees" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in deferred leasing costs</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeferredLeasingFees_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeferredLeasingFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Deferred Leasing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDeferredLeasingFees" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDeferredLeasingFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDeferredLeasingFees" xlink:to="lab_us-gaap_IncreaseDecreaseInDeferredLeasingFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_2a227854-adb1-4c3d-8d0c-d49b747d304e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_5817af5b-32c6-487a-b8aa-76329ca05d58_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_9051f3c4-7d4b-447d-80ab-810ba343d9af_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_0e999202-797e-43a0-ad4c-1bd08818fbc7_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_ea9bd906-706c-496f-b13d-c6be9f8d1bfd_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_b2681815-5701-49ae-8208-5ccee9523fbf_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Distributions in Excess of Earnings</link:label>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Distributions in Excess of Net Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:to="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_2450df22-636d-4744-81e4-eef2c6f68232_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_5e44bf5f-2969-47e2-a34c-a934e044111a_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember_c8ad06ac-ee41-41ea-9cc1-5edd8f39fad2_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST Program, Organization and Offering Fees</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember_label_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Organization and Offering Fees [Member]</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember_documentation_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Organization and Offering Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:to="lab_hgit_RelatedPartyTransactionDSTProgramOrganizationAndOfferingFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_5a14b8c2-5a8d-45bb-8b2f-82cbc0ceb3e3_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ProceedsFromFinancingObligations_491c6b12-49fa-4bcb-a423-ec702f489a75_terseLabel_en-US" xlink:label="lab_hgit_ProceedsFromFinancingObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from financing obligations</link:label>
    <link:label id="lab_hgit_ProceedsFromFinancingObligations_label_en-US" xlink:label="lab_hgit_ProceedsFromFinancingObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Financing Obligations</link:label>
    <link:label id="lab_hgit_ProceedsFromFinancingObligations_documentation_en-US" xlink:label="lab_hgit_ProceedsFromFinancingObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Financing Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ProceedsFromFinancingObligations" xlink:href="hgit-20250930.xsd#hgit_ProceedsFromFinancingObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ProceedsFromFinancingObligations" xlink:to="lab_hgit_ProceedsFromFinancingObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LeasingFeeMember_afa96a46-4f7f-4482-bfff-4255eb822d46_terseLabel_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing Fee</link:label>
    <link:label id="lab_hgit_LeasingFeeMember_label_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasing Fee [Member]</link:label>
    <link:label id="lab_hgit_LeasingFeeMember_documentation_en-US" xlink:label="lab_hgit_LeasingFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leasing Fee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LeasingFeeMember" xlink:href="hgit-20250930.xsd#hgit_LeasingFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LeasingFeeMember" xlink:to="lab_hgit_LeasingFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_acf8198b-0962-48a2-929c-610191ffe5b4_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NoncashOfferingCostsPayable_c64eace0-f5fc-47af-9d64-e5e84c128e9b_terseLabel_en-US" xlink:label="lab_hgit_NoncashOfferingCostsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offering costs payable to the Advisor</link:label>
    <link:label id="lab_hgit_NoncashOfferingCostsPayable_label_en-US" xlink:label="lab_hgit_NoncashOfferingCostsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Offering Costs Payable</link:label>
    <link:label id="lab_hgit_NoncashOfferingCostsPayable_documentation_en-US" xlink:label="lab_hgit_NoncashOfferingCostsPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The noncash increase (decrease) in offering costs. Noncash is defined as transactions during a period that affect recognized assets or liabilities but that do not result in cash receipts or cash payments in the period. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or cash payments in the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NoncashOfferingCostsPayable" xlink:href="hgit-20250930.xsd#hgit_NoncashOfferingCostsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NoncashOfferingCostsPayable" xlink:to="lab_hgit_NoncashOfferingCostsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_6f0a5cf7-dfe7-4b6f-aeee-93eecc00d141_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM OPERATING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_4599c039-00fc-4f67-9636-45d14710a38f_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease, weighted average incremental borrowing rate, percent</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_A185LogisticsMember_54eaf6ab-4f8e-4587-875a-9ecd28b11a2a_terseLabel_en-US" xlink:label="lab_hgit_A185LogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1-85 Logistics Center</link:label>
    <link:label id="lab_hgit_A185LogisticsMember_label_en-US" xlink:label="lab_hgit_A185LogisticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">1-85 Logistics [Member]</link:label>
    <link:label id="lab_hgit_A185LogisticsMember_documentation_en-US" xlink:label="lab_hgit_A185LogisticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">1-85 Logistics</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_A185LogisticsMember" xlink:href="hgit-20250930.xsd#hgit_A185LogisticsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_A185LogisticsMember" xlink:to="lab_hgit_A185LogisticsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss_69a8e75b-9635-4a2d-8aca-fd365821bc05_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain (loss)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesTradingUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ThePeelCentreMember_a541d4ab-9718-4d1e-bb42-bd00e8896a83_terseLabel_en-US" xlink:label="lab_hgit_ThePeelCentreMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Peel Centre</link:label>
    <link:label id="lab_hgit_ThePeelCentreMember_label_en-US" xlink:label="lab_hgit_ThePeelCentreMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The Peel Centre [Member]</link:label>
    <link:label id="lab_hgit_ThePeelCentreMember_documentation_en-US" xlink:label="lab_hgit_ThePeelCentreMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Peel Centre</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ThePeelCentreMember" xlink:href="hgit-20250930.xsd#hgit_ThePeelCentreMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ThePeelCentreMember" xlink:to="lab_hgit_ThePeelCentreMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_962ce1c5-e748-41e8-b201-6a8afc357e8d_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of exchange rate changes on cash, restricted cash and cash equivalents</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_6df1c5bd-959c-4c0a-9c6c-8bb9e3184136_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_49be2768-d618-42b4-b926-25cc23615045_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment property, gross</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, at Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyAtCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ResidentialLivingInvestmentsMember_67300284-9e03-464e-bbfa-fc530e5c083e_terseLabel_en-US" xlink:label="lab_hgit_ResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential/Living investments</link:label>
    <link:label id="lab_hgit_ResidentialLivingInvestmentsMember_label_en-US" xlink:label="lab_hgit_ResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential/Living Investments [Member]</link:label>
    <link:label id="lab_hgit_ResidentialLivingInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_ResidentialLivingInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential/Living Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ResidentialLivingInvestmentsMember" xlink:href="hgit-20250930.xsd#hgit_ResidentialLivingInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ResidentialLivingInvestmentsMember" xlink:to="lab_hgit_ResidentialLivingInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAdditions_040df0b5-175c-4f35-824d-385752240a68_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAdditions" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAdditions_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAdditions" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_40d6383d-86e5-43a8-a050-81e58d9ff143_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_ab681701-0efa-49a8-a189-acc9644c0ab4_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_a4ab2e34-5065-4841-8c7e-33c417c7613d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_6e226c3f-d5cf-439f-87b7-3872b2698057_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash distributions declared per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_000ca6ea-2c18-4890-b9fe-c231d1d02611_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_eb7bd3ae-2d40-425e-afd2-551bdfae152d_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_76a12a23-2d4c-44de-8898-9be5f24b0aaa_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_71769e0f-518c-4fb1-b55a-44243e20b45a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_1e33d3af-8608-42a2-abf6-98f1970f7d63_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs, net</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_759b2823-541f-4b21-b16f-0b1aa39103d7_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total gain (loss) on derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_d5119eec-e7c2-469a-b911-9404ca231337_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMember_395a55b5-7092-43a5-b8bf-72d9dc80f917_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">In-Place Leases</link:label>
    <link:label id="lab_us-gaap_LeasesAcquiredInPlaceMember_label_en-US" xlink:label="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases, Acquired-in-Place [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAcquiredInPlaceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasesAcquiredInPlaceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAcquiredInPlaceMember" xlink:to="lab_us-gaap_LeasesAcquiredInPlaceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_73a60034-06c6-4edc-8a36-cf10ce5e9b6c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_aef3b67f-d15f-4fde-a172-c4cb848bcb1c_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undiscounted Excess Amount</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_4e22c9bc-45f7-4c2f-8c51-7c9bca8c8d30_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_e0dbba24-fac1-4361-9447-4b29b918ba83_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_73bd7b28-38a6-4955-94d2-3623098f6659_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_744fca14-2278-4e69-a339-7f0d5d48a219_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_9ab40154-1bdf-4d76-badb-fac9d9569156_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassSMember_281fbb27-451b-4c41-9f6a-1cce5dc371ec_terseLabel_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class S</link:label>
    <link:label id="lab_hgit_CommonClassSMember_label_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class S [Member]</link:label>
    <link:label id="lab_hgit_CommonClassSMember_documentation_en-US" xlink:label="lab_hgit_CommonClassSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class S [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassSMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassSMember" xlink:to="lab_hgit_CommonClassSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FinancingObligations_4a3ce3ae-5903-4469-afb6-7da91ab20f83_terseLabel_en-US" xlink:label="lab_hgit_FinancingObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing obligations</link:label>
    <link:label id="lab_hgit_FinancingObligations_label_en-US" xlink:label="lab_hgit_FinancingObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Obligations</link:label>
    <link:label id="lab_hgit_FinancingObligations_documentation_en-US" xlink:label="lab_hgit_FinancingObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FinancingObligations" xlink:href="hgit-20250930.xsd#hgit_FinancingObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FinancingObligations" xlink:to="lab_hgit_FinancingObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock_cef8ac91-f950-4bfa-b4d3-8b1b61543a93_terseLabel_en-US" xlink:label="lab_hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Property Revenue in Excess of Property Operating Expenses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock" xlink:href="hgit-20250930.xsd#hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock" xlink:to="lab_hgit_ReconciliationOfPropertyRevenuesInExcessOfExpensesFromSegmentsToConsolidatedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_e0be51b1-c995-4411-baf6-3716952c0c70_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Common Stock Outstanding Roll Forward</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Common Stock Outstanding Roll Forward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_92f0a024-485d-43c3-b11e-a43318d6bf72_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in real estate-related securities</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_70027e05-310c-43a1-a9b8-15b16218cf46_verboseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investments in real estate-related securities</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesDebt" xlink:to="lab_us-gaap_TradingSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_ec453b59-0019-4f22-8220-077aacde8f12_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Schedule of Non-Cash Investing and Financing Activities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_dd839347-2700-41be-abe8-c5be3e419ed7_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_US"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_d88fa2f1-5b89-4e2a-b162-101b3d972852_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets and liabilities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
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    <link:label id="lab_hgit_Junction27Member_463acf1e-3ba3-4af3-8f22-35f1ed85a38f_terseLabel_en-US" xlink:label="lab_hgit_Junction27Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junction 27</link:label>
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    <link:label id="lab_hgit_Junction27Member_documentation_en-US" xlink:label="lab_hgit_Junction27Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junction 27</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_Junction27Member" xlink:href="hgit-20250930.xsd#hgit_Junction27Member"/>
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    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_87a48f80-e5a2-47de-bd9b-16e6658395b9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite Lived Intangible Assets Future Amortization Expense</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
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    <link:label id="lab_hgit_PropertyManagementFeesMember_0adde3b3-8c61-413d-aa02-f54badc4efe1_terseLabel_en-US" xlink:label="lab_hgit_PropertyManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property Management Fees- Hines and its affiliates</link:label>
    <link:label id="lab_hgit_PropertyManagementFeesMember_label_en-US" xlink:label="lab_hgit_PropertyManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Management Fees [Member]</link:label>
    <link:label id="lab_hgit_PropertyManagementFeesMember_documentation_en-US" xlink:label="lab_hgit_PropertyManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Management Fees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PropertyManagementFeesMember" xlink:href="hgit-20250930.xsd#hgit_PropertyManagementFeesMember"/>
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    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_8205406d-7a3a-41b4-988e-b73e14f004d0_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_dae55215-6465-4b09-bf6c-5eea06054028_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average effective interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_960b9b73-f314-4f31-81a4-19ac9f30fd11_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_3534d8e9-b9fa-46db-a63e-1049abb1fb6a_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_8a4dcb87-cfa7-412f-b936-3fc4bc7b9fbc_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, end of period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_ad53a5ef-1135-49cf-b098-79b8066b45a1_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_372bd4a0-2a17-4536-b222-24617bdcde16_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Investments in acquired properties and lease intangibles</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Acquisition, Real Estate, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireRealEstateHeldForInvestment"/>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_5547de8e-5270-4f25-9d3a-3f673fcfe24c_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Benefit (provision) for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_d2f0d016-e151-4167-8650-e5c58250350e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Benefit) provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_DerivativeAssets_3b2c1003-34b7-4c1b-a923-ecbfcaba9f8d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesGlobalREITIIPropertiesLPMember_c52aac6f-3b4e-4ec3-bf2e-b71f0efb9c9a_terseLabel_en-US" xlink:label="lab_hgit_HinesGlobalREITIIPropertiesLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership Partnership</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_8ea0a544-844f-4d96-ac0b-3a41d1e4125d_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of real estate-related securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireMarketableSecurities"/>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_0b94c6c8-9d3b-459d-9345-e57847f0d0a4_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_77a2f25e-bc1c-4049-9a45-ca15ec0d7188_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_74be3aa7-b861-401a-9a43-d0491a049910_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_eb7de654-76cc-4a3f-892b-ecec849ee471_terseLabel_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management fees</link:label>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_542cf000-2381-475f-9305-f7f4175eba9a_verboseLabel_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset management fees</link:label>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_label_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management And Acquisition Fees</link:label>
    <link:label id="lab_hgit_AssetManagementAndAcquisitionFees_documentation_en-US" xlink:label="lab_hgit_AssetManagementAndAcquisitionFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset management and acquisition fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetManagementAndAcquisitionFees" xlink:href="hgit-20250930.xsd#hgit_AssetManagementAndAcquisitionFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetManagementAndAcquisitionFees" xlink:to="lab_hgit_AssetManagementAndAcquisitionFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_5326ec0e-fd03-4ed0-9aa3-47eec1a23e44_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OtherInvestmentMember_79f8bf07-0162-43a4-84c7-6ce7b53708ee_terseLabel_en-US" xlink:label="lab_hgit_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_hgit_OtherInvestmentMember_label_en-US" xlink:label="lab_hgit_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investment [Member]</link:label>
    <link:label id="lab_hgit_OtherInvestmentMember_documentation_en-US" xlink:label="lab_hgit_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OtherInvestmentMember" xlink:href="hgit-20250930.xsd#hgit_OtherInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OtherInvestmentMember" xlink:to="lab_hgit_OtherInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AboveMarketLeasesMember_2f147a9a-ef0a-4748-b67e-0668d00c606e_verboseLabel_en-US" xlink:label="lab_us-gaap_AboveMarketLeasesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Out-of-Market Lease Assets</link:label>
    <link:label id="lab_us-gaap_AboveMarketLeasesMember_label_en-US" xlink:label="lab_us-gaap_AboveMarketLeasesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Above Market Leases [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AboveMarketLeasesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AboveMarketLeasesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AboveMarketLeasesMember" xlink:to="lab_us-gaap_AboveMarketLeasesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_93cddfcd-7c2a-4a70-81b3-b7a892e09ee9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value By Fair Value Hierarchy Level [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_16c72fa0-5033-41dd-adb5-737f8c444df4_negatedTerseLabel_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized financing fees</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_label_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Financing Costs, Net, Permanent Mortgages</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetPermanentMortgages_documentation_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Financing Costs, Net, Permanent Mortgages</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:href="hgit-20250930.xsd#hgit_DeferredFinancingCostsNetPermanentMortgages"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:to="lab_hgit_DeferredFinancingCostsNetPermanentMortgages" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions_abe18c2e-58fd-433b-8f39-0b17a3f1e617_terseLabel_en-US" xlink:label="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of asset acquisitions</link:label>
    <link:label id="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions_label_en-US" xlink:label="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number Of Asset Acquisitions</link:label>
    <link:label id="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions_documentation_en-US" xlink:label="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number Of Asset Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:href="hgit-20250930.xsd#hgit_AssetAcquisitionNumberOfAssetAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:to="lab_hgit_AssetAcquisitionNumberOfAssetAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_dedafae0-61c1-413f-8e3f-5a20b164d6ff_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Stockholders&#8217; Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_97220b4f-06ad-4000-9d65-c361b2303589_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_804979ed-cdf4-42bb-bfb7-86ef48d08d86_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_47852a42-734a-4ece-a8bd-e2a269b07c46_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_9aee1e48-251c-46e3-86d2-b7366eff8ff0_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_d1532aba-63dc-4e01-ba40-3c16bfbaf31c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_95dae90e-bc85-44b3-a07e-df32dc4236b3_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_5992573d-8395-41ec-9e72-c086bc72122b_negatedLabel_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Out-of-Market Lease Intangibles, Net</link:label>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_label_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Liabilities Acquired</link:label>
    <link:label id="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired_documentation_en-US" xlink:label="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Liabilities Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:href="hgit-20250930.xsd#hgit_FiniteLivedIntangibleLiabilitiesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:to="lab_hgit_FiniteLivedIntangibleLiabilitiesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_5fababc3-751c-41b0-a9c2-a773b3f69d8c_terseLabel_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hines Global REIT II Associates LP</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_label_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hines Global REIT II Associates LP [Member]</link:label>
    <link:label id="lab_hgit_HinesGlobalREITIIAssociatesLPMember_documentation_en-US" xlink:label="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hines Global REIT II Associates LP [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:href="hgit-20250930.xsd#hgit_HinesGlobalREITIIAssociatesLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:to="lab_hgit_HinesGlobalREITIIAssociatesLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_6fc75d83-8469-4f32-8523-628ac0e84cd4_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_630d346c-1512-46d0-b544-7ab884f5b0e2_verboseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Buildings and improvements</link:label>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_e4e7f2a7-f38a-4881-908a-9b530cd44c87_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and Improvements</link:label>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_label_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building and Building Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingAndBuildingImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesTable_0194746e-f183-4326-8137-7f04c3f72620_terseLabel_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies [Table]</link:label>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesTable_label_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies [Table]</link:label>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesTable_documentation_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:href="hgit-20250930.xsd#hgit_SummaryofSignificantAccountingPoliciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:to="lab_hgit_SummaryofSignificantAccountingPoliciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesMember_53b1d54f-fe15-4c35-80bd-0b1d8a7a34db_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating rate secured mortgage debt</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesMember" xlink:to="lab_us-gaap_MortgagesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_7136b1e6-70ba-452d-9a4d-1031a474d40b_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths_0def1c31-1a51-4dca-84ee-f059efeb6c06_negatedLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_4eb9312a-f66d-464f-8f54-0aac1e3a900a_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM INVESTING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_0a7f3d0d-0465-49f0-abb9-8468a0e98d8b_verboseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_a08b65a4-1f22-46d6-9c86-f2bcf03e6829_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_da9ed1dd-14f9-4250-9d4c-dfc9bb27de9d_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash from (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_7e945ae4-d408-4f85-8e39-33e00e999075_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes terms (in years)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_76370af5-3af0-46ff-bae3-fc6b1b948105_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassIXMember_26a169ca-ed6f-4e6b-b0a7-e69b7406e39d_terseLabel_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class IX</link:label>
    <link:label id="lab_hgit_CommonClassIXMember_label_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class IX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassIXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassIXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class IX [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassIXMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassIXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassIXMember" xlink:to="lab_hgit_CommonClassIXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_2ed5e063-b2cc-429a-a0c3-ea8b33f9c3e4_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_90fc66a7-60a4-488c-b526-599ac1361b7f_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_4fb3dc88-9ab8-4433-bea5-df9a265b3ae2_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_f92b7fae-cee4-44d3-a2bf-8647d86bf849_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease costs</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_4d8e7665-1796-4629-bf8a-624ee8449d08_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_8f02c203-2a17-4081-98c2-5c2c0cf45f2b_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_91771026-bffb-4e12-b454-b68a1c19eb4b_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Information Regarding Ground Leases</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_38e6e677-1c67-484d-8ac2-6f21369a7710_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SeriesCSeniorNotesMember_bf8909b4-f934-4b77-aae9-217fedf9cce3_terseLabel_en-US" xlink:label="lab_hgit_SeriesCSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C Senior Notes</link:label>
    <link:label id="lab_hgit_SeriesCSeniorNotesMember_label_en-US" xlink:label="lab_hgit_SeriesCSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C Senior Notes [Member]</link:label>
    <link:label id="lab_hgit_SeriesCSeniorNotesMember_documentation_en-US" xlink:label="lab_hgit_SeriesCSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series C Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SeriesCSeniorNotesMember" xlink:href="hgit-20250930.xsd#hgit_SeriesCSeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SeriesCSeniorNotesMember" xlink:to="lab_hgit_SeriesCSeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_7498e4cc-338b-4503-a9c8-e73d9614145e_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_6b15d2bf-c7a3-4fc2-8816-019864aae2f2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fair value derivative instrument, liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_39987361-688f-42cd-be8e-0c3e72eb306c_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_5e6464e0-56e2-4ec7-92ae-a08f20ba228d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement, Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingCostsAndExpensesAbstract_5e880952-7f3a-4040-8ca4-5ec5aae8dc76_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingCostsAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Costs and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingCostsAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingCostsAndExpensesAbstract" xlink:to="lab_us-gaap_OperatingCostsAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_5c3e4636-1bbb-483e-9765-9c1115a2ba88_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_101745d1-c20f-4148-a54a-17686f424748_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions paid to stockholders and noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfOrdinaryDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:to="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_5621cb8e-e193-4e28-85c8-86397918d621_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on sale of real estate</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_d4236471-1a29-42d0-8d1e-1e1ddb46f111_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of real estate</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_e2d752f2-8a4b-4db2-a59c-20eff031fc20_negatedLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Gain) loss on sale of real estate</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gains (Losses) on Sales of Investment Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnSalesOfInvestmentRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:to="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesMember_0ec3ba13-b897-4d32-a174-c9d0035a36bc_terseLabel_en-US" xlink:label="lab_us-gaap_SalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Revenue</link:label>
    <link:label id="lab_us-gaap_SalesMember_label_en-US" xlink:label="lab_us-gaap_SalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesMember" xlink:to="lab_us-gaap_SalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax_98ea8940-ede8-4c53-b9e8-020c53cfc50f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Gain (Loss) Arising During Period, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax"/>
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    <link:label id="lab_dei_EntityAddressStateOrProvince_4b7a1946-be61-44b6-9b3d-ec7cd69c66aa_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_a733d576-dc5b-4433-bfb4-43db884b9e79_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions declared</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_a19de742-37a5-48c4-b6de-57bc2258a7f2_verboseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_58e64e21-da1f-4284-a814-d66b20eeb8f3_totalLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Declared</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_d5bb47f6-98cf-41be-a34c-d5263b078c73_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_a0e24e85-ce0a-4e39-92f0-e3b30a7a8984_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OfficeRealEstateInvestmentsMember_f0c344e3-d236-4472-b86e-f965009f12a0_terseLabel_en-US" xlink:label="lab_hgit_OfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Office investments</link:label>
    <link:label id="lab_hgit_OfficeRealEstateInvestmentsMember_label_en-US" xlink:label="lab_hgit_OfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Office Real Estate Investments [Member]</link:label>
    <link:label id="lab_hgit_OfficeRealEstateInvestmentsMember_documentation_en-US" xlink:label="lab_hgit_OfficeRealEstateInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Domestic Office Real Estate Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OfficeRealEstateInvestmentsMember" xlink:href="hgit-20250930.xsd#hgit_OfficeRealEstateInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OfficeRealEstateInvestmentsMember" xlink:to="lab_hgit_OfficeRealEstateInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_ef07a22c-07fe-47d3-9adc-271bcea973e8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_bcd1d6bb-ac9e-4a32-aa1b-f3245a613b2c_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_a3c4c19c-2351-4585-9aa3-80a316a9be9a_terseLabel_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:label id="lab_dei_EntitiesTable_label_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitiesTable" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitiesTable" xlink:to="lab_dei_EntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_afe11ed7-a9d6-46e0-b67c-8c5364ec27eb_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_0d45eb12-e44a-47de-b467-b29f8cba13d6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash from (used in) investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SellerFinancedDebtMember_96fba318-1814-403e-ae30-dfc6b120e543_terseLabel_en-US" xlink:label="lab_hgit_SellerFinancedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seller-financed debt</link:label>
    <link:label id="lab_hgit_SellerFinancedDebtMember_label_en-US" xlink:label="lab_hgit_SellerFinancedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seller Financed Debt [Member]</link:label>
    <link:label id="lab_hgit_SellerFinancedDebtMember_documentation_en-US" xlink:label="lab_hgit_SellerFinancedDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seller Financed Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SellerFinancedDebtMember" xlink:href="hgit-20250930.xsd#hgit_SellerFinancedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SellerFinancedDebtMember" xlink:to="lab_hgit_SellerFinancedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_b9fa98d9-e8a4-42a4-8d8f-7aaa8f617997_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_570d5fb5-9b93-47d8-bcda-e84809b9a78f_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CreditAgreementMaturingMarch2028Member_3cfaf44a-ea04-4585-a08b-1a9ff188676e_terseLabel_en-US" xlink:label="lab_hgit_CreditAgreementMaturingMarch2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JPMorgan Chase Credit Facility</link:label>
    <link:label id="lab_hgit_CreditAgreementMaturingMarch2028Member_label_en-US" xlink:label="lab_hgit_CreditAgreementMaturingMarch2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Agreement Maturing March 2028 [Member]</link:label>
    <link:label id="lab_hgit_CreditAgreementMaturingMarch2028Member_documentation_en-US" xlink:label="lab_hgit_CreditAgreementMaturingMarch2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Agreement Maturing March 2028</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CreditAgreementMaturingMarch2028Member" xlink:href="hgit-20250930.xsd#hgit_CreditAgreementMaturingMarch2028Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CreditAgreementMaturingMarch2028Member" xlink:to="lab_hgit_CreditAgreementMaturingMarch2028Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_dd5dd262-9be9-41b2-9506-914e07f534e3_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_0361f196-a504-4cad-9ce7-501bbae3ce51_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets, net</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_bc94fea5-aa56-464d-aeb7-73f97b387896_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets, net of accumulated amortization</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_6ba1aa61-ab96-4d8e-9c81-4eba42b9a7cd_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_MontroseCollectiveMember_3bb7b07f-dfb1-4754-8f8b-fb3957546f3f_terseLabel_en-US" xlink:label="lab_hgit_MontroseCollectiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Montrose Collective</link:label>
    <link:label id="lab_hgit_MontroseCollectiveMember_label_en-US" xlink:label="lab_hgit_MontroseCollectiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Montrose Collective [Member]</link:label>
    <link:label id="lab_hgit_MontroseCollectiveMember_documentation_en-US" xlink:label="lab_hgit_MontroseCollectiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Montrose Collective</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_MontroseCollectiveMember" xlink:href="hgit-20250930.xsd#hgit_MontroseCollectiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_MontroseCollectiveMember" xlink:to="lab_hgit_MontroseCollectiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_ef7db8ba-ef15-42d2-9e23-31ecddb60d3b_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease costs</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_7d4f10f6-3927-4777-a735-79a1db5974fa_terseLabel_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution rate per share, per month (in dollars per share)</link:label>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_label_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Dividends Per Share Per Month Declared</link:label>
    <link:label id="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared_documentation_en-US" xlink:label="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Dividends Per Share Per Month Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:href="hgit-20250930.xsd#hgit_CommonStockDividendsPerSharePerMonthDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:to="lab_hgit_CommonStockDividendsPerSharePerMonthDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree_dbd611cd-35b0-4f3a-a0f9-83e5b824e61a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetManagementFeeMember_236be733-9c72-416a-94e4-e7f301801c1b_terseLabel_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management Fees</link:label>
    <link:label id="lab_hgit_AssetManagementFeeMember_label_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management Fee [Member]</link:label>
    <link:label id="lab_hgit_AssetManagementFeeMember_documentation_en-US" xlink:label="lab_hgit_AssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The fee which is equal to a percentage per month of the cost of the Company's real estate investments as of the end of each month. If the Company has determined an estimated net asset value per share, then, with respect to real estate investments included in the board of director's determination, the asset management fees will be calculated using the determined values of such real estate investments at the end of each month.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetManagementFeeMember" xlink:href="hgit-20250930.xsd#hgit_AssetManagementFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetManagementFeeMember" xlink:to="lab_hgit_AssetManagementFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo_dba22773-d67e-4998-ba73-81e3988cd097_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities_64a95207-6ca5-4ac9-b3b2-0215a5a73bb1_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from settlement of interest rate contracts</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Derivative Instrument, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities" xlink:to="lab_us-gaap_ProceedsFromDerivativeInstrumentInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAbstract_6d8ea78f-a987-4aee-b24d-f46f6ed8a13e_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:label id="lab_us-gaap_RealEstateAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAbstract" xlink:to="lab_us-gaap_RealEstateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_IndustrialInvestmentsMember_4db9f83c-04ff-471c-b92f-9cbb6baa7f97_terseLabel_en-US" xlink:label="lab_hgit_IndustrialInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrial investments</link:label>
    <link:label id="lab_hgit_IndustrialInvestmentsMember_label_en-US" xlink:label="lab_hgit_IndustrialInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrial Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_IndustrialInvestmentsMember" xlink:href="hgit-20250930.xsd#hgit_IndustrialInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_IndustrialInvestmentsMember" xlink:to="lab_hgit_IndustrialInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_614d9a54-8381-430f-b488-5ed58f03d94b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_c77b02d3-2bfc-4aa6-9313-cc3ddaab9805_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OutOfMarketLeasesNetMember_7429c599-565a-4c28-89da-bed7045e9d03_terseLabel_en-US" xlink:label="lab_hgit_OutOfMarketLeasesNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Out-of-Market Leases, Net</link:label>
    <link:label id="lab_hgit_OutOfMarketLeasesNetMember_label_en-US" xlink:label="lab_hgit_OutOfMarketLeasesNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Out Of Market Leases Net [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OutOfMarketLeasesNetMember" xlink:href="hgit-20250930.xsd#hgit_OutOfMarketLeasesNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OutOfMarketLeasesNetMember" xlink:to="lab_hgit_OutOfMarketLeasesNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_e3100a32-eef9-44e3-a50a-1eef2546b9dc_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">REPORTABLE SEGMENTS</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_ec75b763-b38e-4848-9adc-a665c23c1a99_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NondesignatedMember_5abd628d-23c5-4cff-9095-445aae9a0ef2_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives not designated as hedging instruments:</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DealerManagerFeeMember_f34a2d06-7550-4aeb-8869-debfa3b0db2a_terseLabel_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dealer Manager Fee</link:label>
    <link:label id="lab_hgit_DealerManagerFeeMember_label_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dealer Manager Fee [Member]</link:label>
    <link:label id="lab_hgit_DealerManagerFeeMember_documentation_en-US" xlink:label="lab_hgit_DealerManagerFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The dealer manager fee based on gross offering proceeds.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DealerManagerFeeMember" xlink:href="hgit-20250930.xsd#hgit_DealerManagerFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DealerManagerFeeMember" xlink:to="lab_hgit_DealerManagerFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable_b672340e-75a6-412f-95eb-ebedb2e26422_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Acquired Finite Lived Intangible Asset Liabilities By Major Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Acquired Finite-Lived Intangible Asset by Major Class [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetByMajorClassTable"/>
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    <link:label id="lab_hgit_NumberOfPropertiesHeldUnderProgram_c7a080e9-f3f8-4825-9515-17daa2589be7_terseLabel_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldUnderProgram" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of properties held under program</link:label>
    <link:label id="lab_hgit_NumberOfPropertiesHeldUnderProgram_label_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldUnderProgram" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Properties Held Under Program</link:label>
    <link:label id="lab_hgit_NumberOfPropertiesHeldUnderProgram_documentation_en-US" xlink:label="lab_hgit_NumberOfPropertiesHeldUnderProgram" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Properties Held Under Program</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NumberOfPropertiesHeldUnderProgram" xlink:href="hgit-20250930.xsd#hgit_NumberOfPropertiesHeldUnderProgram"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_da36cf7e-da20-4eba-ac79-5661a81900c4_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_270eb803-bcac-4d06-aaae-ba167d90ea06_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_4b66eb91-6424-4001-adcc-26070dae8359_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_6d672e1e-7559-488a-ab4d-78f8e7591743_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_c12d5fa4-2007-41be-b0bd-bfe996b401fb_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm_89080096-a2d0-4cf6-ac5a-e6753a223419_terseLabel_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property lease term</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm_label_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement Offerings, Property Lease Term</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm_documentation_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement Offerings, Property Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:href="hgit-20250930.xsd#hgit_PrivatePlacementOfferingsPropertyLeaseTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:to="lab_hgit_PrivatePlacementOfferingsPropertyLeaseTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_e84e5c93-0b81-48f2-9ea6-a3a8456c6ea3_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_7977fa22-132a-4c41-8166-578d7063b67b_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of in-place leases</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_b301989c-1859-4ddc-94d7-7eb4b74360b4_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operating Lease Payments to be Received</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_44f0209a-4149-44dd-843a-ba4575e2650c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Accounting</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_05481ef4-607c-41bd-a578-84cd4bbf1d3a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMiscellaneous" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsMiscellaneous"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMiscellaneous" xlink:to="lab_us-gaap_OtherAssetsMiscellaneous" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SaleOfStockMaximumConsideration_cd18c105-6866-4402-8151-58df59a6acf4_terseLabel_en-US" xlink:label="lab_hgit_SaleOfStockMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum consideration</link:label>
    <link:label id="lab_hgit_SaleOfStockMaximumConsideration_label_en-US" xlink:label="lab_hgit_SaleOfStockMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Maximum Consideration</link:label>
    <link:label id="lab_hgit_SaleOfStockMaximumConsideration_documentation_en-US" xlink:label="lab_hgit_SaleOfStockMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Maximum Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SaleOfStockMaximumConsideration" xlink:href="hgit-20250930.xsd#hgit_SaleOfStockMaximumConsideration"/>
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    <link:label id="lab_us-gaap_StockRedeemedOrCalledDuringPeriodValue_bfd3a98d-831b-46c2-9681-925abdb113f9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRedeemedOrCalledDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemption of common shares</link:label>
    <link:label id="lab_us-gaap_StockRedeemedOrCalledDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRedeemedOrCalledDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Redeemed or Called During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRedeemedOrCalledDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRedeemedOrCalledDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRedeemedOrCalledDuringPeriodValue" xlink:to="lab_us-gaap_StockRedeemedOrCalledDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_8b46fde5-bc85-44e5-a5b2-31d31218db7e_terseLabel_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_label_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:label id="lab_hgit_LongTermDebtMaturityAfterYearFour_documentation_en-US" xlink:label="lab_hgit_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LongTermDebtMaturityAfterYearFour" xlink:href="hgit-20250930.xsd#hgit_LongTermDebtMaturityAfterYearFour"/>
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    <link:label id="lab_us-gaap_PaymentsForCapitalImprovements_065a9a74-a55a-4de9-a3f5-085b61b46f1c_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForCapitalImprovements" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Capital expenditures at operating properties</link:label>
    <link:label id="lab_us-gaap_PaymentsForCapitalImprovements_label_en-US" xlink:label="lab_us-gaap_PaymentsForCapitalImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Capital Improvements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForCapitalImprovements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForCapitalImprovements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForCapitalImprovements" xlink:to="lab_us-gaap_PaymentsForCapitalImprovements" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_4941e99a-72b5-4a5e-9ac6-80c4069465b9_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RecoveryOfDirectCosts_bbde8dfe-fae2-4bee-8a77-81eb4d851138_terseLabel_en-US" xlink:label="lab_us-gaap_RecoveryOfDirectCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recovery revenue</link:label>
    <link:label id="lab_us-gaap_RecoveryOfDirectCosts_label_en-US" xlink:label="lab_us-gaap_RecoveryOfDirectCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Direct Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RecoveryOfDirectCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RecoveryOfDirectCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RecoveryOfDirectCosts" xlink:to="lab_us-gaap_RecoveryOfDirectCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_e13d9446-00c3-4167-afff-e1e5c949fdf5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Revenues from External Customers and Long-Lived Assets [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Revenues from External Customers and Long-Lived Assets [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:to="lab_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherOwnershipInterestsTable_ccd47cbf-644a-4abf-b970-8e6166b5feff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherOwnershipInterestsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Ownership Interests [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherOwnershipInterestsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherOwnershipInterestsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital, Other Ownership Interest [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherOwnershipInterestsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherOwnershipInterestsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherOwnershipInterestsTable" xlink:to="lab_us-gaap_ScheduleOfOtherOwnershipInterestsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_bfd9856f-e9c8-4504-b5e6-255d53c2307b_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNet_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNet" xlink:to="lab_us-gaap_BelowMarketLeaseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_8d3db8ea-783e-440c-8869-766492cbef0f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long Term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_bd6000b1-ce54-47ac-a911-f8cf4779caa4_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_6c82cabc-cf43-4584-b130-4723911ca8d6_verboseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_20a43c5b-aaeb-4ac6-a924-14c92e37a86e_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Disclosure of Cash Flow Information</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Elements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowElementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_f98d84aa-a708-448b-9ac0-b8c17f74fd25_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolver</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAbstract_403829b4-1b02-41d6-899b-d255f231e8e8_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss):</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAbstract_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_6d633bd9-0982-4cd6-afd8-bcdde7837064_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_39f1bda1-f8f2-4dae-b53c-3be42e1fc0e7_netLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Financing lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_d22178ad-8891-4812-9cc1-68f2e4ec5908_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ground Lease Liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_83799ea0-750a-411c-8542-b4fd594f1c38_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_f0bb0791-3b02-49bb-b4a7-b55aaa006c93_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage_ce7c10ba-f90d-4f95-895b-43ccb781cccf_terseLabel_en-US" xlink:label="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance participation allocation, subject to annual return percentage</link:label>
    <link:label id="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage_label_en-US" xlink:label="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Incentive Rate, Subject To Required Return Percentage</link:label>
    <link:label id="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage_documentation_en-US" xlink:label="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Incentive Rate, Subject To Required Return Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:href="hgit-20250930.xsd#hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:to="lab_hgit_ManagementAndServiceFeesIncentiveRateSubjectToRequiredReturnPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_0c550cd3-6e4b-40a7-8c9e-d7b6fc7c6441_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_89add8a9-e497-497d-a622-94a6a3bc3c7d_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_b18a34ea-9641-428c-b424-7ea0a57e38d7_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_12c4a2e8-ee29-49be-bd7b-66bc01aa91c4_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other investing activities</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_f6ad9d6b-4aab-410d-9181-e43c00eac2ca_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember_b94e19a8-fbfe-4a15-b8e4-a388ab3bb0ac_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST Program, Upfront Dealer Manager Fees</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember_label_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Upfront Dealer Manager Fees [Member]</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember_documentation_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Upfront Dealer Manager Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:to="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontDealerManagerFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SellingCommissionsMember_54ccdcd6-9cd1-409f-9186-1dabb4b42e35_terseLabel_en-US" xlink:label="lab_hgit_SellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling Commissions</link:label>
    <link:label id="lab_hgit_SellingCommissionsMember_label_en-US" xlink:label="lab_hgit_SellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling Commissions [Member]</link:label>
    <link:label id="lab_hgit_SellingCommissionsMember_documentation_en-US" xlink:label="lab_hgit_SellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Selling Commissions [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SellingCommissionsMember" xlink:href="hgit-20250930.xsd#hgit_SellingCommissionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SellingCommissionsMember" xlink:to="lab_hgit_SellingCommissionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_TortonaLogisticsMember_dac8ef50-e17f-4a86-b6ab-09ca475dcefa_terseLabel_en-US" xlink:label="lab_hgit_TortonaLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tortona Logistics</link:label>
    <link:label id="lab_hgit_TortonaLogisticsMember_label_en-US" xlink:label="lab_hgit_TortonaLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tortona Logistics [Member]</link:label>
    <link:label id="lab_hgit_TortonaLogisticsMember_documentation_en-US" xlink:label="lab_hgit_TortonaLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tortona Logistics</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_TortonaLogisticsMember" xlink:href="hgit-20250930.xsd#hgit_TortonaLogisticsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_TortonaLogisticsMember" xlink:to="lab_hgit_TortonaLogisticsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffMarketLeaseUnfavorable_0a4ed88b-2fcd-4371-9848-3605990edb64_terseLabel_en-US" xlink:label="lab_us-gaap_OffMarketLeaseUnfavorable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible lease liabilities, net</link:label>
    <link:label id="lab_us-gaap_OffMarketLeaseUnfavorable_label_en-US" xlink:label="lab_us-gaap_OffMarketLeaseUnfavorable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Market Lease, Unfavorable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffMarketLeaseUnfavorable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffMarketLeaseUnfavorable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffMarketLeaseUnfavorable" xlink:to="lab_us-gaap_OffMarketLeaseUnfavorable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_4d396f69-160e-4ca5-b04a-40f3db31ba0f_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DealerManagerMember_e4c7895e-e627-4052-864b-b29ce3311426_terseLabel_en-US" xlink:label="lab_hgit_DealerManagerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dealer Manager</link:label>
    <link:label id="lab_hgit_DealerManagerMember_label_en-US" xlink:label="lab_hgit_DealerManagerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dealer Manager [Member]</link:label>
    <link:label id="lab_hgit_DealerManagerMember_documentation_en-US" xlink:label="lab_hgit_DealerManagerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Dealer Manager, Hines Securities, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DealerManagerMember" xlink:href="hgit-20250930.xsd#hgit_DealerManagerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DealerManagerMember" xlink:to="lab_hgit_DealerManagerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_8c133645-a37e-41ec-80f5-04412a6ccec7_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_2d93d552-dc8d-4158-9cf6-cbb33da3c792_terseLabel_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonrelated Party</link:label>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonrelated Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonrelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrelatedPartyMember" xlink:to="lab_us-gaap_NonrelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_c35dc112-b5e1-4784-b3e1-5eb8065f5fec_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_ace6d94c-f0d0-4f3a-9edc-afaf7c8aaa67_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_31c51c23-60fd-42ed-981e-a2eb8e51242d_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">FAIR VALUE MEASUREMENTS</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_be0ca12e-2bbe-4b2e-baf2-5a69f860a40a_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_e39d625e-f6d6-498c-ae5e-65cd910b52db_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_a48b1545-b2fc-4b25-97a7-8dda0fec8e61_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_5c40ab06-e7ae-4874-b707-12c85da03178_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_79d5e053-7889-4b39-bfde-299118d3b129_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_809f99a8-98a5-43d5-a84e-930f31cb8043_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering_ae82e121-62ad-466c-923d-3e570aea5989_terseLabel_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Length of agreement prior to closing of offering (in years)</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering_label_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement Offering, Length Of Agreement Prior To Closing of Offering</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering_documentation_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement Offering, Length Of Agreement Prior To Closing of Offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:href="hgit-20250930.xsd#hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:to="lab_hgit_PrivatePlacementOfferingLengthOfAgreementPriorToClosingOfOffering" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear_9a2cf46d-4c1e-469d-b735-33d58a2ffc90_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_f49199d7-aed5-40b9-b243-81467f834cf0_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_a283bcf2-22a0-4a3d-9d41-7415bf1778c1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_ae3247a4-21ae-4949-aa85-d420b0fa36d6_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_2456db2a-9ec7-40bc-801d-a9454839d877_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DERIVATIVE INSTRUMENTS</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_b78ea118-57ab-4310-87ac-3ac63b0cbaa1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_39d4b0c5-fe49-4c1a-8a70-441957c3d55d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value derivative instrument, assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_d901ff7c-ba19-4c6f-8da5-8bca2bb7befa_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name of Property [Domain]</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Name of Property [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:to="lab_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNet_c8a0d3b5-e955-4e70-a7dd-56e84c370594_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_c04e86ca-e583-4f53-8592-b0306697f438_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ConstructionManagementFeesMember_7600306c-5baf-4725-ac8d-a1c45b5e37c9_terseLabel_en-US" xlink:label="lab_hgit_ConstructionManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Development and Construction Management Fees</link:label>
    <link:label id="lab_hgit_ConstructionManagementFeesMember_label_en-US" xlink:label="lab_hgit_ConstructionManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction Management Fees [Member]</link:label>
    <link:label id="lab_hgit_ConstructionManagementFeesMember_documentation_en-US" xlink:label="lab_hgit_ConstructionManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Construction Management Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ConstructionManagementFeesMember" xlink:href="hgit-20250930.xsd#hgit_ConstructionManagementFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ConstructionManagementFeesMember" xlink:to="lab_hgit_ConstructionManagementFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems_6315b1bf-6c41-4f63-a9cb-7eeedbc2184d_terseLabel_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies [Line Items]</link:label>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems_label_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies [Line Items]</link:label>
    <link:label id="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems_documentation_en-US" xlink:label="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Summary of Significant Accounting Policies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:href="hgit-20250930.xsd#hgit_SummaryofSignificantAccountingPoliciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:to="lab_hgit_SummaryofSignificantAccountingPoliciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassTXMember_9c66245a-a883-4a36-bece-2fb63178f8dd_terseLabel_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class TX</link:label>
    <link:label id="lab_hgit_CommonClassTXMember_label_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class TX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassTXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassTXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class TX [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassTXMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassTXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassTXMember" xlink:to="lab_hgit_CommonClassTXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_857418ce-42fc-4d9c-a1a2-41307edf179b_totalLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_CostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RunwayRetailMember_999e1642-9b69-494c-b8b8-13c2ca4c95ed_terseLabel_en-US" xlink:label="lab_hgit_RunwayRetailMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Runway - Retail</link:label>
    <link:label id="lab_hgit_RunwayRetailMember_label_en-US" xlink:label="lab_hgit_RunwayRetailMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Runway - Retail [Member]</link:label>
    <link:label id="lab_hgit_RunwayRetailMember_documentation_en-US" xlink:label="lab_hgit_RunwayRetailMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Runway - Retail</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RunwayRetailMember" xlink:href="hgit-20250930.xsd#hgit_RunwayRetailMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RunwayRetailMember" xlink:to="lab_hgit_RunwayRetailMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_7b2d7c5a-160e-4a46-b985-0f9f8e7e0fd6_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_6972d374-c42b-4eaf-874a-f04dc70bd5e5_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_aaa917d1-335b-48ac-a4cc-59c0b06fe6bf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Offering costs</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Stock Issued, Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_14294aa1-9040-4d74-bcd8-91855ab8f731_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_country_CZ_46c9b877-cfcc-45fa-8fda-7a5c3135993d_terseLabel_en-US" xlink:label="lab_country_CZ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Czech Republic</link:label>
    <link:label id="lab_country_CZ_label_en-US" xlink:label="lab_country_CZ" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CZECHIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CZ" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CZ"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_CZ" xlink:to="lab_country_CZ" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_MonthlyAssetManagementFeeMember_7d4305f2-a8df-4027-b0fe-478688cc99e3_terseLabel_en-US" xlink:label="lab_hgit_MonthlyAssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Monthly Asset Management Fee</link:label>
    <link:label id="lab_hgit_MonthlyAssetManagementFeeMember_label_en-US" xlink:label="lab_hgit_MonthlyAssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Monthly Asset Management Fee [Member]</link:label>
    <link:label id="lab_hgit_MonthlyAssetManagementFeeMember_documentation_en-US" xlink:label="lab_hgit_MonthlyAssetManagementFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Monthly Asset Management Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_MonthlyAssetManagementFeeMember" xlink:href="hgit-20250930.xsd#hgit_MonthlyAssetManagementFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_MonthlyAssetManagementFeeMember" xlink:to="lab_hgit_MonthlyAssetManagementFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_edea9dba-402c-4b11-b1b2-91a1e20fe32f_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FloatingRateSecuredMortgageDebtMember_5ec759b3-2109-4732-94a2-c709f2a6555f_terseLabel_en-US" xlink:label="lab_hgit_FloatingRateSecuredMortgageDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating rate secured mortgage debt</link:label>
    <link:label id="lab_hgit_FloatingRateSecuredMortgageDebtMember_label_en-US" xlink:label="lab_hgit_FloatingRateSecuredMortgageDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Floating Rate Secured Mortgage Debt [Member]</link:label>
    <link:label id="lab_hgit_FloatingRateSecuredMortgageDebtMember_documentation_en-US" xlink:label="lab_hgit_FloatingRateSecuredMortgageDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Floating Rate Secured Mortgage Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FloatingRateSecuredMortgageDebtMember" xlink:href="hgit-20250930.xsd#hgit_FloatingRateSecuredMortgageDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FloatingRateSecuredMortgageDebtMember" xlink:to="lab_hgit_FloatingRateSecuredMortgageDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_country_DE_3fa97ce7-7edf-4fa4-92da-1c59f9c563e4_terseLabel_en-US" xlink:label="lab_country_DE" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Germany</link:label>
    <link:label id="lab_country_DE_label_en-US" xlink:label="lab_country_DE" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GERMANY</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_DE" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_DE"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_DE" xlink:to="lab_country_DE" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_8b4c2bd5-0a69-4337-ac1b-af8ed7c3aa3e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_369cd8dd-1e49-46b2-b5d8-d9e1836b0fab_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OtherLiabilitiesOffset_ff3a9e01-6403-4979-a279-5499cbf429a1_negatedTerseLabel_en-US" xlink:label="lab_hgit_OtherLiabilitiesOffset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Expense reimbursements</link:label>
    <link:label id="lab_hgit_OtherLiabilitiesOffset_label_en-US" xlink:label="lab_hgit_OtherLiabilitiesOffset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Offset</link:label>
    <link:label id="lab_hgit_OtherLiabilitiesOffset_documentation_en-US" xlink:label="lab_hgit_OtherLiabilitiesOffset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OtherLiabilitiesOffset" xlink:href="hgit-20250930.xsd#hgit_OtherLiabilitiesOffset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OtherLiabilitiesOffset" xlink:to="lab_hgit_OtherLiabilitiesOffset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_febb40b7-cd83-418d-9094-34ffe5ab061e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Contracts</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Derivatives [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_ed1b656d-3284-4959-8b5d-9d121c0d6fc7_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_e53406bc-fcde-44e6-bc76-b055aa7d4025_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_9ca143b0-b9e7-4cf6-b235-b12ca5cd68db_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_0cec978f-bab3-4158-99d0-5665a023f642_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_3520f98b-01ab-4b25-9891-5fced328ebb3_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_77bfce1f-f9b4-4156-a982-23a2f80102a8_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_702792ce-4993-4e85-ad61-5d85d54e8f21_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_6e0d3927-9b7a-4894-b060-0b6db968165d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate_7fb10832-6110-4726-8bd1-c20e11699c67_negatedTerseLabel_en-US" xlink:label="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Provision for income taxes related to sale of real estate</link:label>
    <link:label id="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate_3b35a836-2e2b-4c53-9856-115edad3820c_terseLabel_en-US" xlink:label="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for income taxes related to sale of real estate</link:label>
    <link:label id="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate_label_en-US" xlink:label="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Sale Of Real Estate</link:label>
    <link:label id="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate_documentation_en-US" xlink:label="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Sale Of Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:href="hgit-20250930.xsd#hgit_IncomeTaxExpenseBenefitSaleOfRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:to="lab_hgit_IncomeTaxExpenseBenefitSaleOfRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_1b4d4aa4-87b1-427d-a29b-31483c0100e4_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">INVESTMENT PROPERTY</link:label>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:to="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_MaintalLogisticsMember_dbee7cf6-fdf3-46c1-a0f3-08c37d7ade36_terseLabel_en-US" xlink:label="lab_hgit_MaintalLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maintal Logistics</link:label>
    <link:label id="lab_hgit_MaintalLogisticsMember_label_en-US" xlink:label="lab_hgit_MaintalLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maintal Logistics [Member]</link:label>
    <link:label id="lab_hgit_MaintalLogisticsMember_documentation_en-US" xlink:label="lab_hgit_MaintalLogisticsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maintal Logistics - Investment Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_MaintalLogisticsMember" xlink:href="hgit-20250930.xsd#hgit_MaintalLogisticsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_MaintalLogisticsMember" xlink:to="lab_hgit_MaintalLogisticsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonClassTMember_7feca2b3-4e9c-4193-8164-baa5c6c016b9_terseLabel_en-US" xlink:label="lab_hgit_CommonClassTMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class T</link:label>
    <link:label id="lab_hgit_CommonClassTMember_label_en-US" xlink:label="lab_hgit_CommonClassTMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class T [Member]</link:label>
    <link:label id="lab_hgit_CommonClassTMember_documentation_en-US" xlink:label="lab_hgit_CommonClassTMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Classification of common stock that has different rights than provided to Class A, or general common stock shares, representing ownership interest in a corporation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassTMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassTMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CommonClassTMember" xlink:to="lab_hgit_CommonClassTMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LeftBankMember_1028a6ee-740d-4525-9e6c-94ec461e4694_terseLabel_en-US" xlink:label="lab_hgit_LeftBankMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Left Bank</link:label>
    <link:label id="lab_hgit_LeftBankMember_label_en-US" xlink:label="lab_hgit_LeftBankMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Left Bank [Member]</link:label>
    <link:label id="lab_hgit_LeftBankMember_documentation_en-US" xlink:label="lab_hgit_LeftBankMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Left Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LeftBankMember" xlink:href="hgit-20250930.xsd#hgit_LeftBankMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LeftBankMember" xlink:to="lab_hgit_LeftBankMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember_187635a4-8c14-4c38-91ed-dab855143ea5_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST Program, Upfront Selling Commissions</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember_label_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Upfront Selling Commissions [Member]</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember_documentation_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Upfront Selling Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:to="lab_hgit_RelatedPartyTransactionDSTProgramUpfrontSellingCommissionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_2ef0e129-2d3f-484c-860d-457787e73ca1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionLineItems" xlink:to="lab_us-gaap_AssetAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_432d55a6-e5ed-4b0b-ad07-5e7826ae2503_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenues:</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_799a1443-5553-4eae-98f2-50d3c7e8faf3_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_4ac15daf-a0e5-428a-bb62-663efb5381e5_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of common shares</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_eedd9221-9137-4a0b-9846-ffc2bacd43a4_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finance Lease, Liability, to be Paid, Maturity</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_FinanceLeaseCostAbstract_f61e8b92-131d-4c21-a60f-ea220a906e32_terseLabel_en-US" xlink:label="lab_hgit_FinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease costs</link:label>
    <link:label id="lab_hgit_FinanceLeaseCostAbstract_label_en-US" xlink:label="lab_hgit_FinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost [Abstract]</link:label>
    <link:label id="lab_hgit_FinanceLeaseCostAbstract_documentation_en-US" xlink:label="lab_hgit_FinanceLeaseCostAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_FinanceLeaseCostAbstract" xlink:href="hgit-20250930.xsd#hgit_FinanceLeaseCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_FinanceLeaseCostAbstract" xlink:to="lab_hgit_FinanceLeaseCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_ba93f9b9-76c1-48c6-b98c-a8f43a2b886b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_10208ccb-4de6-420c-be13-5fea195ad3c6_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_HinesMember_c7537e14-fdcb-4987-88ef-193534fde5c8_verboseLabel_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Hines and Affiliates</link:label>
    <link:label id="lab_hgit_HinesMember_label_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hines [Member]</link:label>
    <link:label id="lab_hgit_HinesMember_documentation_en-US" xlink:label="lab_hgit_HinesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Name of the related party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_HinesMember" xlink:href="hgit-20250930.xsd#hgit_HinesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_HinesMember" xlink:to="lab_hgit_HinesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_9f3c9832-37e5-4c9a-8188-b0ea8871e6f3_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NetRentableAreaLeasedPercentage_ddc7012b-04b0-464e-a6c4-21f72997659b_terseLabel_en-US" xlink:label="lab_hgit_NetRentableAreaLeasedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net rentable area leased (in percent)</link:label>
    <link:label id="lab_hgit_NetRentableAreaLeasedPercentage_label_en-US" xlink:label="lab_hgit_NetRentableAreaLeasedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Rentable Area Leased, Percentage</link:label>
    <link:label id="lab_hgit_NetRentableAreaLeasedPercentage_documentation_en-US" xlink:label="lab_hgit_NetRentableAreaLeasedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Rentable Area Leased, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NetRentableAreaLeasedPercentage" xlink:href="hgit-20250930.xsd#hgit_NetRentableAreaLeasedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NetRentableAreaLeasedPercentage" xlink:to="lab_hgit_NetRentableAreaLeasedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_49765eef-1812-4df5-8731-6fbd4eeb3cc7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements Fair Value Hierarchy Domain</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RentReceivablesMember_31060c52-e6ef-40e5-ba04-8f65fb930e22_terseLabel_en-US" xlink:label="lab_hgit_RentReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rent Receivables</link:label>
    <link:label id="lab_hgit_RentReceivablesMember_label_en-US" xlink:label="lab_hgit_RentReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rent Receivables [Member]</link:label>
    <link:label id="lab_hgit_RentReceivablesMember_documentation_en-US" xlink:label="lab_hgit_RentReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rent Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RentReceivablesMember" xlink:href="hgit-20250930.xsd#hgit_RentReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RentReceivablesMember" xlink:to="lab_hgit_RentReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_cd743ada-419f-434b-b156-110c3131ddcd_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_1be0cf78-2a0e-4d7c-889a-36059933691e_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_StatutoryTrustProgramLineItems_d5e1f0e4-b0e8-46bf-b882-8f1c42e3357f_terseLabel_en-US" xlink:label="lab_hgit_StatutoryTrustProgramLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Trust Program [Line Items]</link:label>
    <link:label id="lab_hgit_StatutoryTrustProgramLineItems_label_en-US" xlink:label="lab_hgit_StatutoryTrustProgramLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Trust Program [Line Items]</link:label>
    <link:label id="lab_hgit_StatutoryTrustProgramLineItems_documentation_en-US" xlink:label="lab_hgit_StatutoryTrustProgramLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Statutory Trust Program</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_StatutoryTrustProgramLineItems" xlink:href="hgit-20250930.xsd#hgit_StatutoryTrustProgramLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_StatutoryTrustProgramLineItems" xlink:to="lab_hgit_StatutoryTrustProgramLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_0915057a-9fb1-4506-b4c1-7a705002c4ec_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on notes payable</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfNotesPayable" xlink:to="lab_us-gaap_RepaymentsOfNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_b5845504-5298-4d48-bcc0-d1292a4c456d_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_a814c1c8-da79-4808-ac44-a5234dd4a851_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DEBT FINANCING</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_96796973-bdee-48e8-a2d6-6b288fc2939d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred shares, $0.001 par value per share; 500,000 preferred shares authorized, none issued or outstanding as of September&#160;30, 2025 and December&#160;31, 2024</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsMember_6797d052-3460-4eaa-a8c4-02d4d7bedc15_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_AssetsMember_label_en-US" xlink:label="lab_us-gaap_AssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsMember" xlink:to="lab_us-gaap_AssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_5dd59e50-ffd2-406a-9261-aba27adc8d98_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_d3e5ca32-69cc-465e-817a-781cd355c2b0_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteAbstract" xlink:to="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_17302a37-43c0-44f1-ab9d-06e2d9041345_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, $0.001 par value per share (Note 7)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_16ec78b9-ec9f-4c3c-8de1-871e2f22574b_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease right-of-use asset, net</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_2224c123-ba49-47d9-ac3a-7d7add991fa5_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financing lease right-of-use assets, net of accumulated amortization</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CostofRealEstateInvestmentsPerMonthMember_6e067ac9-b67e-4d01-a942-506fa7f393a9_terseLabel_en-US" xlink:label="lab_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of real estate investments per month</link:label>
    <link:label id="lab_hgit_CostofRealEstateInvestmentsPerMonthMember_label_en-US" xlink:label="lab_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Real Estate Investments Per Month [Member]</link:label>
    <link:label id="lab_hgit_CostofRealEstateInvestmentsPerMonthMember_documentation_en-US" xlink:label="lab_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cost of Real Estate Investments Per Month [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:href="hgit-20250930.xsd#hgit_CostofRealEstateInvestmentsPerMonthMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:to="lab_hgit_CostofRealEstateInvestmentsPerMonthMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_844ee051-1dcd-4474-a7ff-1e7752ea24cf_verboseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">COMMITMENTS AND CONTINGENCIES</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_939b4215-0c44-4b81-b6de-20055b582438_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares outstanding, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_0a4ad364-d6b3-4c16-ada7-e9c04828b073_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reportable Segments</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_d65f39d2-f104-4844-a3fb-0f825298ab07_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 12)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DistributionandStockholderServicingExpenseMember_5556d397-8134-4d1f-bf0a-4e185a50aa80_verboseLabel_en-US" xlink:label="lab_hgit_DistributionandStockholderServicingExpenseMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Distribution and Stockholder Servicing Fees</link:label>
    <link:label id="lab_hgit_DistributionandStockholderServicingExpenseMember_label_en-US" xlink:label="lab_hgit_DistributionandStockholderServicingExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distribution and Stockholder Servicing Expense [Member]</link:label>
    <link:label id="lab_hgit_DistributionandStockholderServicingExpenseMember_documentation_en-US" xlink:label="lab_hgit_DistributionandStockholderServicingExpenseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distribution and Stockholder Servicing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DistributionandStockholderServicingExpenseMember" xlink:href="hgit-20250930.xsd#hgit_DistributionandStockholderServicingExpenseMember"/>
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    <link:label id="lab_us-gaap_DerivativeTable_307eba73-6ece-4670-a2e4-11d202f805e9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_5faf0d7c-0a7d-4ddc-b964-309f9f3bcaeb_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_aea75feb-f7af-4ceb-a4c7-17ce68cc46a5_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NumberOfProperties_6dac28e9-e12b-4594-9545-6098f9def6f2_terseLabel_en-US" xlink:label="lab_hgit_NumberOfProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of properties</link:label>
    <link:label id="lab_hgit_NumberOfProperties_label_en-US" xlink:label="lab_hgit_NumberOfProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Properties</link:label>
    <link:label id="lab_hgit_NumberOfProperties_documentation_en-US" xlink:label="lab_hgit_NumberOfProperties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NumberOfProperties" xlink:href="hgit-20250930.xsd#hgit_NumberOfProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NumberOfProperties" xlink:to="lab_hgit_NumberOfProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_87797270-d35c-42bd-a7eb-42a3449c90af_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of offering costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_b1050708-e0d2-47df-b264-08203fef1c3a_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interests</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_bb447746-ffe6-4070-aa1c-cd185a17850e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive_dcfec707-6bd6-40fa-8403-a978ed98f554_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_ab24bce0-b329-4034-ba32-c948a7878fba_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetRentableArea_2dd8a538-3c76-40da-a1f0-46add990becd_terseLabel_en-US" xlink:label="lab_us-gaap_NetRentableArea" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net rentable area (in sqft)</link:label>
    <link:label id="lab_us-gaap_NetRentableArea_label_en-US" xlink:label="lab_us-gaap_NetRentableArea" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Rentable Area</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetRentableArea" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetRentableArea"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetRentableArea" xlink:to="lab_us-gaap_NetRentableArea" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_e55e7e63-3a4a-4b9f-a530-ea5008264fdc_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThereafter" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_e6bba38e-f167-4326-ac86-045504e2e034_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsLineItems_5a846dc2-cf33-446a-9342-194438723337_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions [Line Items]</link:label>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsLineItems_label_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Ownership Interests [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOwnershipInterestsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherOwnershipInterestsLineItems"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_b6bb8f56-2ac9-41ec-a211-e3094760465d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_fb090d01-0048-44ad-b179-126bb719a5b2_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_ba7c9039-ab4f-4f69-92c6-c2173d5eded9_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
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    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationAxis"/>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionTableTextBlock_d1641b27-c044-48ae-9cd7-97247b549819_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Purchase Price for Acquisitions</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_971aba3e-97d6-43ec-8404-9642f0871e69_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
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    <link:label id="lab_dei_DocumentType_adc2fb58-7156-435c-a66e-ad6f0a2ce887_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_243e30c7-64e0-4d98-810f-f5a687f22169_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
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    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_DerivativeNumberOfInstrumentsHeld_5b3791c1-ce84-4ca6-885e-c1017d4299f7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Contracts</link:label>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_9f2cba35-8d38-48ce-bdb3-fc0af43dc6cd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
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    <link:label id="lab_country_ES_50d383dd-5e3e-4abd-a627-e1d3ea9fa233_terseLabel_en-US" xlink:label="lab_country_ES" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spain</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_15f2a0d4-0ace-463b-8bd0-fdc43dc40fc1_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of common shares</link:label>
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    <link:label id="lab_us-gaap_LessorOperatingLeaseTermOfContract_bfb1f619-3101-4e16-b98a-a0f9476b2177_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease terms (in years)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyTransactionDSTProgramMember" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyTransactionDSTProgramMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyTransactionDSTProgramMember" xlink:to="lab_hgit_RelatedPartyTransactionDSTProgramMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_e27b8fdd-a526-4ca6-a53c-f0bb58eed3aa_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, amount of hedged item</link:label>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_label_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Amount of Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAmountOfHedgedItem"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:to="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_702506ca-d5a8-4b51-adba-3669daa3d339_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_182aa3dc-ad15-41c6-82b0-a3645738ce19_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_8ba7f2bd-d49d-4faf-b92d-d0e71de20421_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net purchase price</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_9a8f68d5-bc88-4028-ac17-e716b1f4cf49_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contract purchase price</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionConsiderationTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_2f814922-b9b5-44bd-aba6-d18b215afd42_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Gain) loss on derivative instruments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_68317aeb-4b31-45eb-9d08-40f198e62f36_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_7873426c-56cb-4572-9e96-b1d44b07c19a_verboseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">In-place Lease Intangibles</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_7b4e9ed7-d41f-4ea6-b3d3-e4123b6f4f7c_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change in due to affiliates</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Due to Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDueToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:to="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan_29043c05-bfff-485d-9544-c6e628059bdc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions reinvested</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStockDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_60a8550b-c1b3-458f-9f34-e496f6bad643_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, weighted average interest rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ProceedsFromPaymentsForSecurityDeposit_6a0ba25c-1053-4f32-8db9-6833ead26144_terseLabel_en-US" xlink:label="lab_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in security deposit liability</link:label>
    <link:label id="lab_hgit_ProceedsFromPaymentsForSecurityDeposit_label_en-US" xlink:label="lab_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From (Payments For) Security Deposit</link:label>
    <link:label id="lab_hgit_ProceedsFromPaymentsForSecurityDeposit_documentation_en-US" xlink:label="lab_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From (Payments For) Security Deposit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:href="hgit-20250930.xsd#hgit_ProceedsFromPaymentsForSecurityDeposit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:to="lab_hgit_ProceedsFromPaymentsForSecurityDeposit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_OtherFeesMember_da81343a-82af-4e49-baa2-39e3034661c2_terseLabel_en-US" xlink:label="lab_hgit_OtherFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Fees</link:label>
    <link:label id="lab_hgit_OtherFeesMember_label_en-US" xlink:label="lab_hgit_OtherFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Fees [Member]</link:label>
    <link:label id="lab_hgit_OtherFeesMember_documentation_en-US" xlink:label="lab_hgit_OtherFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Fees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_OtherFeesMember" xlink:href="hgit-20250930.xsd#hgit_OtherFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_OtherFeesMember" xlink:to="lab_hgit_OtherFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_9f5d9671-9bab-4d78-86b9-e8ea37f640d2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivatePlacementMember_02f5632d-bbfa-4ffa-9f02-2b7c18dd91a5_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
    <link:label id="lab_us-gaap_PrivatePlacementMember_label_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrivatePlacementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivatePlacementMember" xlink:to="lab_us-gaap_PrivatePlacementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_251a9026-1637-4d34-bf95-3e231c2ca233_negatedTerseLabel_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in tenant and other receivables</link:label>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_label_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase Decrease In Tenant And Other Receivables</link:label>
    <link:label id="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables_documentation_en-US" xlink:label="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The increase (decrease) during the reporting period in tenant and other receivables.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:href="hgit-20250930.xsd#hgit_IncreaseDecreaseInTenantAndOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:to="lab_hgit_IncreaseDecreaseInTenantAndOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable_29204c4d-aadc-4db0-8594-e08342a94d88_terseLabel_en-US" xlink:label="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution and stockholder servicing fees payable to the Dealer Manager</link:label>
    <link:label id="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable_label_en-US" xlink:label="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non Cash Increase (Decrease) In Distribution and Stockholder Servicing Fees Payable</link:label>
    <link:label id="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable_documentation_en-US" xlink:label="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The noncash increase (decrease) in selling commissions, dealer manager fees, and distribution and stockholder servicing fees payable. Noncash is defined as transactions during a period that affect recognized assets or liabilities but that do not result in cash receipts or cash payments in the period. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or cash payments in the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:href="hgit-20250930.xsd#hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:to="lab_hgit_NonCashIncreaseDecreaseInDistributionAndStockholderServicingFeesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_187aa523-7f55-4431-acea-fe80c6a2d762_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cost</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseGross_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseGross" xlink:to="lab_us-gaap_BelowMarketLeaseGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_070735f5-7f04-4b42-a989-0367d8f8c4cd_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from notes payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromNotesPayable" xlink:to="lab_us-gaap_ProceedsFromNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_a8fa1da4-e985-4d1e-8c76-896a5806df71_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_9f1f9b20-71ab-4695-b8ae-f14a27a71d40_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_055bc548-a111-433a-9215-d11611d4da1b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Gain (Loss) on Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_09027893-5017-476a-856b-183a1c379d2e_negatedTerseLabel_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Selling commissions, dealer manager fees and distribution and stockholder servicing fees</link:label>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_label_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling Commissions, Dealer Manager Fees, And Distribution And Stockholder Servicing Fees</link:label>
    <link:label id="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_documentation_en-US" xlink:label="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Selling commissions, dealer manager fees, and distribution and stockholder servicing fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:href="hgit-20250930.xsd#hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:to="lab_hgit_SellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_5001180e-b518-46e4-9879-0ab9fd1a1979_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices In Active Markets for Identical Items (Level 1)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_29907a3e-74f1-4a23-88af-5cdf00e1f5d9_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency gains (losses)</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_2148f69d-6a82-481e-a633-5626f58421a0_negatedLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Foreign currency (gains) losses</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_604a7dfb-a38a-4a53-a800-4325a4ac41fd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_92ab28ad-13fe-4472-bf7b-61497791c98b_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted income (loss) per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_d7cc8fa8-81ff-4646-af11-c5301204da60_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_a8a30059-4bf1-41fb-bd42-e0f8813e3c4c_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFiveYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_a0ae0c9a-ce0d-4abf-902a-90da9eae15f7_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetAcquisitionRightOfUseAssetNet_e1605e38-503d-459e-b9a9-5e36ee17dd17_terseLabel_en-US" xlink:label="lab_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right of Use Asset, Net</link:label>
    <link:label id="lab_hgit_AssetAcquisitionRightOfUseAssetNet_label_en-US" xlink:label="lab_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Right Of Use Asset, Net</link:label>
    <link:label id="lab_hgit_AssetAcquisitionRightOfUseAssetNet_documentation_en-US" xlink:label="lab_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Right Of Use Asset, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:href="hgit-20250930.xsd#hgit_AssetAcquisitionRightOfUseAssetNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:to="lab_hgit_AssetAcquisitionRightOfUseAssetNet" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm_a06fb8a3-0f0f-43bb-b184-1ac28e496d7d_terseLabel_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period to acquire interest on program (in months)</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm_label_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement Offerings, Duration To Acquire Beneficial Interest On Program, Term</link:label>
    <link:label id="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm_documentation_en-US" xlink:label="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement Offerings, Duration To Acquire Beneficial Interest On Program, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:href="hgit-20250930.xsd#hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:to="lab_hgit_PrivatePlacementOfferingsDurationToAcquireBeneficialInterestOnProgramTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyFeePercentage_7485b985-d841-45e0-b58c-15a865f6f941_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party fee, percent</link:label>
    <link:label id="lab_hgit_RelatedPartyFeePercentage_label_en-US" xlink:label="lab_hgit_RelatedPartyFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Fee, Percentage</link:label>
    <link:label id="lab_hgit_RelatedPartyFeePercentage_documentation_en-US" xlink:label="lab_hgit_RelatedPartyFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Identifies the stated percentage per the agreement, for example, asset management and acquisition fees between related parties.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyFeePercentage" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyFeePercentage" xlink:to="lab_hgit_RelatedPartyFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidInsurance_e1d858ee-7aba-4c5d-afc6-48ad0ef9028c_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid insurance</link:label>
    <link:label id="lab_us-gaap_PrepaidInsurance_label_en-US" xlink:label="lab_us-gaap_PrepaidInsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidInsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidInsurance" xlink:to="lab_us-gaap_PrepaidInsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_5bc217f2-cdb4-4456-9540-6be5e53a8ed2_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss):</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_LesseeOperatingLeaseNumberOfAgreements_a6976793-3e28-41c7-9e88-83ed302b655f_terseLabel_en-US" xlink:label="lab_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of agreements accounted for as operating leases</link:label>
    <link:label id="lab_hgit_LesseeOperatingLeaseNumberOfAgreements_label_en-US" xlink:label="lab_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Agreements</link:label>
    <link:label id="lab_hgit_LesseeOperatingLeaseNumberOfAgreements_documentation_en-US" xlink:label="lab_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:href="hgit-20250930.xsd#hgit_LesseeOperatingLeaseNumberOfAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:to="lab_hgit_LesseeOperatingLeaseNumberOfAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_277c01bf-373b-424d-81e8-7c9086ea1365_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_bb0cd55e-73a6-4784-9051-28838e0eaefc_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_WorshipSquareMember_ec470136-94a5-484a-8b0e-591a66a7af63_terseLabel_en-US" xlink:label="lab_hgit_WorshipSquareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Worship Square</link:label>
    <link:label id="lab_hgit_WorshipSquareMember_label_en-US" xlink:label="lab_hgit_WorshipSquareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Worship Square [Member]</link:label>
    <link:label id="lab_hgit_WorshipSquareMember_documentation_en-US" xlink:label="lab_hgit_WorshipSquareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Worship Square</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_WorshipSquareMember" xlink:href="hgit-20250930.xsd#hgit_WorshipSquareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_WorshipSquareMember" xlink:to="lab_hgit_WorshipSquareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour_dd5a5e29-f11d-4fda-a1cb-cb1224742f9a_negatedLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Amortization Income, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseAmortizationIncomeYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour" xlink:to="lab_us-gaap_BelowMarketLeaseAmortizationIncomeYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_5636fa5d-f7d3-4587-9c46-93cc3909d182_terseLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total revenues in excess of property operating expenses</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_64e0c579-0796-40f8-94bc-0d8253ee6778_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTable" xlink:to="lab_us-gaap_AssetAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SeriesDESeniorNotesMember_fefbd3fc-7241-4613-897e-7ed27f6e6a9d_terseLabel_en-US" xlink:label="lab_hgit_SeriesDESeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D/E Senior Notes</link:label>
    <link:label id="lab_hgit_SeriesDESeniorNotesMember_label_en-US" xlink:label="lab_hgit_SeriesDESeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D/E Senior Notes [Member]</link:label>
    <link:label id="lab_hgit_SeriesDESeniorNotesMember_documentation_en-US" xlink:label="lab_hgit_SeriesDESeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D/E Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SeriesDESeniorNotesMember" xlink:href="hgit-20250930.xsd#hgit_SeriesDESeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SeriesDESeniorNotesMember" xlink:to="lab_hgit_SeriesDESeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives_4b303221-b283-40e1-ae8a-ceb4e2347d07_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives_label_en-US" xlink:label="lab_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Methods of Accounting, Derivatives Not Designated or Qualifying as Hedges [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives" xlink:to="lab_us-gaap_DerivativesMethodsOfAccountingNonhedgingDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_7c849e7e-197e-41cd-a465-62576b4b2b54_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undiscounted Excess Amount</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_4807d239-3fa7-4d63-ab4d-b3b16f633fc7_negatedTerseLabel_en-US" xlink:label="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of selling commissions, dealer manager fees and distribution and stockholder servicing fees</link:label>
    <link:label id="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_label_en-US" xlink:label="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Of Selling Commissions, Dealer Manager Fees and Distribution and Stockholder Servicing Fees</link:label>
    <link:label id="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees_documentation_en-US" xlink:label="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment Of Selling Commissions, Dealer Manager Fees And Distribution And Stockholder Servicing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:href="hgit-20250930.xsd#hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:to="lab_hgit_PaymentOfSellingCommissionsDealerManagerFeesAndDistributionAndStockholderServicingFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_c1e536ae-b217-4fae-b23f-ac58bd82b4ac_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_f7eb2cdf-befb-48cc-80a4-b14d8c2f3d1a_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RedemptionsIncurredButNotYetPaid_a41825b7-2692-4e9b-a3d8-bda00ff6c374_terseLabel_en-US" xlink:label="lab_hgit_RedemptionsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares tendered for redemption</link:label>
    <link:label id="lab_hgit_RedemptionsIncurredButNotYetPaid_label_en-US" xlink:label="lab_hgit_RedemptionsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redemptions Incurred But Not Yet Paid</link:label>
    <link:label id="lab_hgit_RedemptionsIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_hgit_RedemptionsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redemptions Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RedemptionsIncurredButNotYetPaid" xlink:href="hgit-20250930.xsd#hgit_RedemptionsIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RedemptionsIncurredButNotYetPaid" xlink:to="lab_hgit_RedemptionsIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_8067244d-44ad-4c06-b01c-4f60a7c17ac1_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock_8773b8a1-b4c4-4afb-ab95-b1242dd74574_terseLabel_en-US" xlink:label="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of additional classes of shares of common stock</link:label>
    <link:label id="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock_label_en-US" xlink:label="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Additional Classes Of Stock</link:label>
    <link:label id="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock_documentation_en-US" xlink:label="lab_hgit_CommonStockNumberOfAdditionalClassesOfStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Additional Classes Of Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonStockNumberOfAdditionalClassesOfStock" xlink:href="hgit-20250930.xsd#hgit_CommonStockNumberOfAdditionalClassesOfStock"/>
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    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_d3f4ddc0-bbc7-4ba0-bcef-52906e559be0_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt outstanding</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_6ee67cb2-7a5a-438f-bd0e-47c4fa75b1de_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Principal Outstanding</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative_7e73ec0f-413b-46ef-bd43-c28e24083efe_terseLabel_en-US" xlink:label="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative shares issued (in shares)</link:label>
    <link:label id="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative_label_en-US" xlink:label="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number Of Shares Issued In Transaction, Cumulative</link:label>
    <link:label id="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative_documentation_en-US" xlink:label="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement Offerings, Net Proceeds, In Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:href="hgit-20250930.xsd#hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:to="lab_hgit_SaleOfStockNumberOfSharesIssuedInTransactionCumulative" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PublicOfferingsMember_018d7216-430e-4b40-8f04-1e542946b7f7_terseLabel_en-US" xlink:label="lab_hgit_PublicOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public Offerings</link:label>
    <link:label id="lab_hgit_PublicOfferingsMember_label_en-US" xlink:label="lab_hgit_PublicOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public Offerings [Member]</link:label>
    <link:label id="lab_hgit_PublicOfferingsMember_documentation_en-US" xlink:label="lab_hgit_PublicOfferingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Offerings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PublicOfferingsMember" xlink:href="hgit-20250930.xsd#hgit_PublicOfferingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PublicOfferingsMember" xlink:to="lab_hgit_PublicOfferingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_f6b76400-218f-45ab-ac75-d4249c15c150_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Gain (Loss) on Investments in Real Estate-Related Securities</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestmentsTextBlock" xlink:to="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_20c97122-2626-4ca5-95b7-47e524f976b8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Frequency Domain</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_bf3947c4-fed9-4b90-8edc-1be60dbd207a_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_IssuerCostsMember_c0a131e5-6d1c-417d-a690-a717075c3d42_terseLabel_en-US" xlink:label="lab_hgit_IssuerCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization and Offering Costs- the Advisor</link:label>
    <link:label id="lab_hgit_IssuerCostsMember_label_en-US" xlink:label="lab_hgit_IssuerCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Issuer Costs [Member]</link:label>
    <link:label id="lab_hgit_IssuerCostsMember_documentation_en-US" xlink:label="lab_hgit_IssuerCostsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Issuer Costs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_IssuerCostsMember" xlink:href="hgit-20250930.xsd#hgit_IssuerCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_IssuerCostsMember" xlink:to="lab_hgit_IssuerCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_c112790d-3d5d-4ad2-9c8b-b8bc09207e55_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">STOCKHOLDERS' EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectOperatingCosts_89391a5c-7855-47f3-9573-b61abbf8b337_terseLabel_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property operating expenses</link:label>
    <link:label id="lab_us-gaap_DirectOperatingCosts_label_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Operating Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectOperatingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectOperatingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectOperatingCosts" xlink:to="lab_us-gaap_DirectOperatingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_5d338df6-04f9-4f26-abbc-79150ca5f020_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_49a1ef95-510f-4838-bd69-3b162fa8eeac_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on derivative instruments</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_f6af64e2-8aef-4f4e-b344-bfd47dcd2c00_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Gain) loss on derivative instruments</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
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    <link:label id="lab_hgit_CommonClassAXMember_a8f0d1c9-739f-4d5d-a1da-46b4e755dad2_terseLabel_en-US" xlink:label="lab_hgit_CommonClassAXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class AX</link:label>
    <link:label id="lab_hgit_CommonClassAXMember_label_en-US" xlink:label="lab_hgit_CommonClassAXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class AX [Member]</link:label>
    <link:label id="lab_hgit_CommonClassAXMember_documentation_en-US" xlink:label="lab_hgit_CommonClassAXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Class AX [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_CommonClassAXMember" xlink:href="hgit-20250930.xsd#hgit_CommonClassAXMember"/>
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    <link:label id="lab_us-gaap_SubsequentEventTable_0de15b50-77f8-4e2f-9a56-638e78bb6cfd_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_c8114e13-0a7e-483b-8cc3-2abed61b3916_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in progress</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionInProgressMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConstructionInProgressMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressMember" xlink:to="lab_us-gaap_ConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_67a950aa-a294-4724-914c-dade739e1bce_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment property, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_032d0ded-3bb8-4e90-bb88-0d0f0cc26c8a_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Investment property, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_74ec2f49-2848-4fa5-b85f-73ae08a44756_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_8af1686f-95fd-450c-9961-cad8e948c6dc_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_fd5bb364-c972-494a-9ba0-da9315fd6af7_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, amount</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_9e655f55-b429-4aec-bb7c-63e638dfbd9e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, fees and expense reimbursements incurred</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_d756b852-87fe-45f3-b5ea-ff8836177534_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_46fca0b8-08bd-4d03-8d23-ef8ec015a6d2_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_36e3e3bd-8999-471f-895d-4eff0806114d_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk</link:label>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeographicConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeographicConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeographicConcentrationRiskMember" xlink:to="lab_us-gaap_GeographicConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_987fe909-867e-4c7d-b56b-a7f58dd39783_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemption of common shares</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_UptonCrossingMember_7a15ba39-2a4c-43fe-84c4-ea471b8caf16_terseLabel_en-US" xlink:label="lab_hgit_UptonCrossingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upton Crossing</link:label>
    <link:label id="lab_hgit_UptonCrossingMember_label_en-US" xlink:label="lab_hgit_UptonCrossingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Upton Crossing [Member]</link:label>
    <link:label id="lab_hgit_UptonCrossingMember_documentation_en-US" xlink:label="lab_hgit_UptonCrossingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Upton Crossing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_UptonCrossingMember" xlink:href="hgit-20250930.xsd#hgit_UptonCrossingMember"/>
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    <link:label id="lab_dei_EntityCurrentReportingStatus_c2efddbb-4766-483e-8a58-66b28657d4ff_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesIncentiveRate_82d54e3b-baa8-46be-b908-abe4a37389ba_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance participation allocation percentage</link:label>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesIncentiveRate_label_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Incentive Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ManagementAndServiceFeesIncentiveRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:to="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_0837a50a-b8f8-4ec3-ae68-b51bf94b73ad_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_285dcf39-dd26-4e0c-84f8-808ce7185924_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net amortization of out-of-market leases, increase to rental revenue</link:label>
    <link:label id="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases_label_en-US" xlink:label="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of above and below Market Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfAboveAndBelowMarketLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:to="lab_us-gaap_AmortizationOfAboveAndBelowMarketLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_42a07716-6e33-4de4-a7c1-869e7387dc2c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_0e212ae0-00c8-4f64-b35b-ea4160042848_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name of Property [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis"/>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_f6cff877-9c1c-476b-a996-b76adc3d07ee_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember_7e60f219-61e6-482e-83a5-1542d37cca54_terseLabel_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST Program, Ongoing Fees</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember_label_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Dealer Manager Ongoing Fees [Member]</link:label>
    <link:label id="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember_documentation_en-US" xlink:label="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, DST Program, Dealer Manager Ongoing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:href="hgit-20250930.xsd#hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:to="lab_hgit_RelatedPartyTransactionDSTProgramDealerManagerOngoingFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock_80aaedcb-856c-436e-986b-9ac15d08c0e5_terseLabel_en-US" xlink:label="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DST PROGRAM</link:label>
    <link:label id="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock_label_en-US" xlink:label="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Beneficial Interest Private Placement Offerings [Text Block]</link:label>
    <link:label id="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock_documentation_en-US" xlink:label="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Beneficial Interest Private Placement Offerings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:href="hgit-20250930.xsd#hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:to="lab_hgit_BeneficialInterestPrivatePlacementOfferingsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_GeorgiaInternationalTradeCenterMember_3b542b23-5152-4283-8ac4-92610dd99a69_terseLabel_en-US" xlink:label="lab_hgit_GeorgiaInternationalTradeCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Georgia International Trade Center</link:label>
    <link:label id="lab_hgit_GeorgiaInternationalTradeCenterMember_label_en-US" xlink:label="lab_hgit_GeorgiaInternationalTradeCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Georgia International Trade Center [Member]</link:label>
    <link:label id="lab_hgit_GeorgiaInternationalTradeCenterMember_documentation_en-US" xlink:label="lab_hgit_GeorgiaInternationalTradeCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Georgia International Trade Center</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_GeorgiaInternationalTradeCenterMember" xlink:href="hgit-20250930.xsd#hgit_GeorgiaInternationalTradeCenterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_GeorgiaInternationalTradeCenterMember" xlink:to="lab_hgit_GeorgiaInternationalTradeCenterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_7bcced24-aa52-429b-be89-430a7167f10e_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest percentage (less than)</link:label>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_label_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Liability Company or Limited Partnership, Members or Limited Partners, Ownership Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:to="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_086cf2a5-ba0f-401a-9d9f-c059053100ac_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_87a62757-b1b7-492d-9009-8d702ab35151_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_country_IE_52d4bef1-3ab3-4dd7-aeb7-e0274615d05c_terseLabel_en-US" xlink:label="lab_country_IE" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ireland</link:label>
    <link:label id="lab_country_IE_label_en-US" xlink:label="lab_country_IE" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IRELAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_IE" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_IE"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_IE" xlink:to="lab_country_IE" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_65cda6a6-dfda-408e-81e0-009a458794a0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_096e5b9e-b328-4bcc-8ad3-e5ad00a24b55_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_e8ca2e3c-aea9-46c0-b83a-221d3bb2f353_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems_f1881764-76f1-4b69-86d2-527cde37b664_terseLabel_en-US" xlink:label="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property Subject To Or Available For Operating Lease</link:label>
    <link:label id="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems_label_en-US" xlink:label="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Lessor Asset under Operating Lease [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems" xlink:to="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_c8c8231d-a2f2-4d54-bba2-3240c61ab057_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income and expenses</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_4069ef95-6704-43f9-852c-f078df4e240c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other income and expenses</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_6d3436e9-7380-4bcf-80da-809d6c9cd713_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_992da47d-0a8c-48f2-afc9-f662cfac52f2_verboseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income (loss) to net cash from (used in) operating activities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_f1e1e89e-89a7-4b6d-a11c-7507385c4400_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM FINANCING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome_2343e04b-dedc-427f-b080-6447995eb934_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDistributionsInExcessOfNetIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated distributions in excess of earnings</link:label>
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    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
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    <link:label id="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities_240fb06e-92c3-4865-b1bc-9b08936d0f1f_terseLabel_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs, net</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities_label_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Financing Costs, Net, Revolving Credit Facilities</link:label>
    <link:label id="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities_documentation_en-US" xlink:label="lab_hgit_DeferredFinancingCostsNetRevolvingCreditFacilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Financing Costs, Net, Revolving Credit Facilities</link:label>
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    <link:label id="lab_us-gaap_InterestRateContractMember_4bcdcde9-9f66-4dad-9379-10edab099849_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate contracts</link:label>
    <link:label id="lab_us-gaap_InterestRateContractMember_label_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateContractMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateContractMember"/>
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    <link:label id="lab_hgit_PrivatePlacementNotesMember_331ed345-6281-487d-8de1-cd775be2e067_terseLabel_en-US" xlink:label="lab_hgit_PrivatePlacementNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private placement note issuances</link:label>
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    <link:label id="lab_hgit_PrivatePlacementNotesMember_documentation_en-US" xlink:label="lab_hgit_PrivatePlacementNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PrivatePlacementNotesMember" xlink:href="hgit-20250930.xsd#hgit_PrivatePlacementNotesMember"/>
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    <link:label id="lab_country_IT_24da9cab-292d-4e5c-be82-0ca68c510ed7_terseLabel_en-US" xlink:label="lab_country_IT" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Italy</link:label>
    <link:label id="lab_country_IT_label_en-US" xlink:label="lab_country_IT" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ITALY</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingInformationProfitLossAbstract_14d74ec3-137b-4b4b-b786-e5d3591a67fb_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationProfitLossAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information, Profit (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationProfitLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:to="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DepreciationAndAmortization1_191d21d3-02e9-464d-8396-a22329919195_terseLabel_en-US" xlink:label="lab_hgit_DepreciationAndAmortization1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_hgit_DepreciationAndAmortization1_label_en-US" xlink:label="lab_hgit_DepreciationAndAmortization1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation and amortization 1</link:label>
    <link:label id="lab_hgit_DepreciationAndAmortization1_documentation_en-US" xlink:label="lab_hgit_DepreciationAndAmortization1" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The current period expense charged against earnings on long-lived, physical assets not used in production, and which are not intended for resale, to allocate or recognize the cost of such assets over their useful lives; or to record the reduction in book value of an intangible asset over the benefit period of such asset; or to reflect consumption during the period of an asset that is not used in production. Differs from the amount on the income statement due to the amortization of deferred financing costs and out of market leases that are recorded elsewhere on the cash flow statement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DepreciationAndAmortization1" xlink:href="hgit-20250930.xsd#hgit_DepreciationAndAmortization1"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_a9d4c105-7de8-4792-8d25-84c2d21fdbaa_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from settlement of real estate-related securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities"/>
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    <link:label id="lab_us-gaap_BelowMarketLeaseNetAbstract_0a0fdc3e-1ac4-4f38-89eb-a5de4489fd0a_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Out-of-Market Lease Liabilities</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAbstract_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNetAbstract" xlink:to="lab_us-gaap_BelowMarketLeaseNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_f699dbb3-2a60-4bae-be60-c3798ec88651_verboseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">ORGANIZATION</link:label>
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    <link:label id="lab_us-gaap_PaymentsForDerivativeInstrumentInvestingActivities_d3c1ba4c-135f-4c50-90c3-02b83634c7b3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments related to interest rate contracts</link:label>
    <link:label id="lab_us-gaap_PaymentsForDerivativeInstrumentInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Derivative Instrument, Investing Activities</link:label>
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    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_4ad651da-76fd-48b8-9433-35ab94a7a651_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_country_PL_10bd1dca-d20d-4dbf-ab87-cf98b1c64876_terseLabel_en-US" xlink:label="lab_country_PL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Poland</link:label>
    <link:label id="lab_country_PL_label_en-US" xlink:label="lab_country_PL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">POLAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_PL" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_PL"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_8efc3573-0acc-4f7c-b578-88ca191d98f0_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock_c58d1d79-9aaf-466b-b58b-a936caf10d74_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Acquired Finite-Lived Intangible Assets By Major Class</link:label>
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    <link:label id="lab_hgit_AdvisorMember_aa63dc7e-c3e4-4372-9ea6-00cbfc544755_terseLabel_en-US" xlink:label="lab_hgit_AdvisorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Advisor</link:label>
    <link:label id="lab_hgit_AdvisorMember_label_en-US" xlink:label="lab_hgit_AdvisorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The Advisor [Member]</link:label>
    <link:label id="lab_hgit_AdvisorMember_documentation_en-US" xlink:label="lab_hgit_AdvisorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Advisor, Hines Global REIT II Advisors LP [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AdvisorMember" xlink:href="hgit-20250930.xsd#hgit_AdvisorMember"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_5aec2770-16b1-4239-935e-7d68ce817087_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate</link:label>
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    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_f2aaefda-e3e0-4a3a-a492-5a6c762c8279_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash from (used in) financing activities</link:label>
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    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
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    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_35b1ddc1-a0bd-4b3d-927e-548dace9a694_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average incremental borrowing rate, percent</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_22c9247f-7bd0-49eb-89b1-513b447ad577_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredRentReceivablesNet_c1e9d33a-fcfe-4f4c-a524-56223cc90f7a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredRentReceivablesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Straight-line rent receivable</link:label>
    <link:label id="lab_us-gaap_DeferredRentReceivablesNet_label_en-US" xlink:label="lab_us-gaap_DeferredRentReceivablesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Rent Receivables, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredRentReceivablesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredRentReceivablesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredRentReceivablesNet" xlink:to="lab_us-gaap_DeferredRentReceivablesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_11ef47a6-c7e4-4d8e-9766-e62792741514_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets Measured on Recurring Basis</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_ff065b93-1eff-4b37-8d67-e86d2e9dc45a_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares outstanding, basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_us-gaap_CashFlowSupplementalDisclosuresTextBlock_a6816857-0f93-497b-9a53-0a68505ef364_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowSupplementalDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUPPLEMENTAL CASH FLOW DISCLOSURES</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_ba037168-0c12-43e0-be63-80a7b1f989ee_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventsAbstract_5166f417-5e84-4f83-8e17-6d2bf7b4cc57_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_383e0a3f-5274-4d76-9734-fb49776047b2_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract_e2651d7c-dec7-428f-b2ec-14504f9e3d46_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">In-Place Lease</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestExpenseRelatedToPerformanceFees_1180c5da-3160-4b2c-9720-72a6a34790b5_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseRelatedToPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance participation allocation</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseRelatedToPerformanceFees_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseRelatedToPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense Related to Performance Fees</link:label>
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    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_8b0f2d93-56b7-424c-9007-f76bd328b228_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument</link:label>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_bb15083c-fd91-44ee-9f7c-c24f04381a32_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred financing costs</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_9368a700-4262-41ca-b100-e5539aef4883_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expenses):</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_cfb94b89-a16e-4b00-821a-962b2c629b01_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_ef4c4f8f-2861-42b6-b137-90f497a29e85_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_5bc1cdc6-b8f5-493b-bbfd-e6562d26eac7_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionAxis" xlink:to="lab_us-gaap_AssetAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable_92bea387-caab-48fb-9105-77ed61fde5b6_terseLabel_en-US" xlink:label="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property Subject To Or Available For Operating Lease By Major Property Class [Table]</link:label>
    <link:label id="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable_label_en-US" xlink:label="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Lessor Asset under Operating Lease [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable" xlink:to="lab_us-gaap_PropertySubjectToOrAvailableForOperatingLeaseByMajorPropertyClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_840b3791-f390-4527-a233-73cbbd065695_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of direct real estate investments owned</link:label>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_label_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfRealEstateProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfRealEstateProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfRealEstateProperties" xlink:to="lab_us-gaap_NumberOfRealEstateProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_8f41f311-f96b-4a70-ae46-3b484b0b726b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain (loss)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesTradingRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative_96189bff-dfce-41cf-9291-df6cd3d97c6b_terseLabel_en-US" xlink:label="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative offering proceeds</link:label>
    <link:label id="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative_label_en-US" xlink:label="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received On Transaction, Cumulative</link:label>
    <link:label id="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative_documentation_en-US" xlink:label="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received On Transaction, Cumulative</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:href="hgit-20250930.xsd#hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:to="lab_hgit_SaleOfStockConsiderationReceivedOnTransactionCumulative" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_3511ae83-5523-4c50-be45-dd5d304d3cbd_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_2409540f-18df-4a5f-8908-4ebbc521d8f6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_ManagementFeeWaivedPercentage_59a1cb3e-bb12-4c29-9ebb-4980ec5e847a_terseLabel_en-US" xlink:label="lab_hgit_ManagementFeeWaivedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee waived, percent</link:label>
    <link:label id="lab_hgit_ManagementFeeWaivedPercentage_label_en-US" xlink:label="lab_hgit_ManagementFeeWaivedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee, Waived, Percentage</link:label>
    <link:label id="lab_hgit_ManagementFeeWaivedPercentage_documentation_en-US" xlink:label="lab_hgit_ManagementFeeWaivedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fee, Waived, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_ManagementFeeWaivedPercentage" xlink:href="hgit-20250930.xsd#hgit_ManagementFeeWaivedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_ManagementFeeWaivedPercentage" xlink:to="lab_hgit_ManagementFeeWaivedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_PerformanceParticipationAllocationMember_50f78bf8-3724-4fe0-a6ad-e78c3fd762f9_terseLabel_en-US" xlink:label="lab_hgit_PerformanceParticipationAllocationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation</link:label>
    <link:label id="lab_hgit_PerformanceParticipationAllocationMember_label_en-US" xlink:label="lab_hgit_PerformanceParticipationAllocationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation [Member]</link:label>
    <link:label id="lab_hgit_PerformanceParticipationAllocationMember_documentation_en-US" xlink:label="lab_hgit_PerformanceParticipationAllocationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_PerformanceParticipationAllocationMember" xlink:href="hgit-20250930.xsd#hgit_PerformanceParticipationAllocationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_PerformanceParticipationAllocationMember" xlink:to="lab_hgit_PerformanceParticipationAllocationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_ac7a0fac-1dbc-4de7-b36f-eefed932f605_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_02b08889-6393-48d3-a2e7-85f87baaaa38_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_DebtWeightedAverageYearsToMaturity_47c39d13-bc93-4fec-87cb-cad6abd90ba6_terseLabel_en-US" xlink:label="lab_hgit_DebtWeightedAverageYearsToMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, weighted average years to maturity (in years)</link:label>
    <link:label id="lab_hgit_DebtWeightedAverageYearsToMaturity_label_en-US" xlink:label="lab_hgit_DebtWeightedAverageYearsToMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Years To Maturity</link:label>
    <link:label id="lab_hgit_DebtWeightedAverageYearsToMaturity_documentation_en-US" xlink:label="lab_hgit_DebtWeightedAverageYearsToMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted average years to maturity related to the entity's debt in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_DebtWeightedAverageYearsToMaturity" xlink:href="hgit-20250930.xsd#hgit_DebtWeightedAverageYearsToMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_DebtWeightedAverageYearsToMaturity" xlink:to="lab_hgit_DebtWeightedAverageYearsToMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_54ad9067-8de6-4f21-97b1-f321a8a76ab1_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_44877af0-0c57-428a-a4be-3f4a1c0b9034_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rental revenue</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract_531d4f6a-6566-4e7b-ac1a-856b60e87905_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Future Minimum Rentals</link:label>
    <link:label id="lab_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Leases, Future Minimum Payments Receivable [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract" xlink:to="lab_us-gaap_OperatingLeasesFutureMinimumPaymentsReceivableAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_27e41278-1353-4299-9e4a-71ce4004f1ff_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_7e97c413-1ea6-4899-864a-a955f761c191_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUBSEQUENT EVENTS</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_5db3450a-367f-42e8-a38c-7827a9c653a0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_57a5098b-d397-434a-89a3-1bda7404219c_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate-level accounts</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_country_NL_5cf9fa26-38c1-46d7-a32e-b2794b01ffff_terseLabel_en-US" xlink:label="lab_country_NL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Netherlands</link:label>
    <link:label id="lab_country_NL_label_en-US" xlink:label="lab_country_NL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NETHERLANDS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_NL" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_NL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_NL" xlink:to="lab_country_NL" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract_d7de7e92-f001-4227-b827-078629b21397_terseLabel_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Out-of-Market Leases, Net</link:label>
    <link:label id="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Below Market Lease, Net, Amortization Income, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:to="lab_us-gaap_BelowMarketLeaseNetAmortizationIncomeFiscalYearMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_290acd75-a5fa-484d-8b75-eb17fb35422f_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">October 1, 2025 through December 31, 2025</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_0f07007a-88c5-4422-b7fa-3c3f219090ce_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_be0437ab-7faa-4084-9fe1-cbbe2b224da2_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet_ec8fb3e7-ccf0-407d-b824-2e5356b06f6f_totalLabel_en-US" xlink:label="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Assets Acquired And Liabilities Assumed, Net</link:label>
    <link:label id="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet_documentation_en-US" xlink:label="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Assets Acquired And Liabilities Assumed, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:href="hgit-20250930.xsd#hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:to="lab_hgit_AssetAcquisitionAssetsAcquiredAndLiabilitiesAssumedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_cfb18bff-76a8-4d3e-8e7f-00bdfc8f4674_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued capital additions</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_f2dabd68-2476-4717-b6a1-47be8341efe5_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum Capacity in Functional Currency</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_hgit_TermLoanFacilityMember_52b109b5-6ac5-4f50-86e6-7823338fe569_terseLabel_en-US" xlink:label="lab_hgit_TermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loans</link:label>
    <link:label id="lab_hgit_TermLoanFacilityMember_label_en-US" xlink:label="lab_hgit_TermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Loan Facility [Member]</link:label>
    <link:label id="lab_hgit_TermLoanFacilityMember_documentation_en-US" xlink:label="lab_hgit_TermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_hgit_TermLoanFacilityMember" xlink:href="hgit-20250930.xsd#hgit_TermLoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_hgit_TermLoanFacilityMember" xlink:to="lab_hgit_TermLoanFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_ce071b70-2500-408b-aa9a-c646f46b4e43_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_1fcfe9f8-e7a5-4747-bfd3-1c231694aedf_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation_51283ef5-f1b2-4440-afb7-76e77fac580e_negatedLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_88088e6b-1c67-41ae-9199-87a6aef1fb2a_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Leases</link:label>
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