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Mortgage Payable and Other Secured Financing - Contractual Maturities of Mortgages Payable and Other Secured Financing (Details) - USD ($) | Mar. 31, 2023 | Dec. 31, 2022
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Mortgage Loans On Real Estate [Line Items] |  |
Total mortgages payable and other secured financings, net | $ 1,690,000 | $ 1,690,000

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- Definition Mortgages payable and other secured financing, net. + References No definition available. + Details
Name: | ghi_MortgagesPayableAndOtherSecuredFinancingNet
Namespace Prefix: | ghi_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | srt_MortgageLoansOnRealEstateLineItems
Namespace Prefix: | srt_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration