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Fair Value of Financial Instruments - Additional Information (Details) - USD ($) | Sep. 30, 2023 | Dec. 31, 2022 | Sep. 30, 2022 | Dec. 31, 2021
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Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |  |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 515,304,516 | $ 667,698,183 |  |
Fair Value, Inputs, Level 3 [Member] | Governmental Issuer Loan [Member] |  |  |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |  |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 257,600,000 | $ 305,000,000 | $ 11,300,000 | $ 6,800,000

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- Definition Available for Sale Security and Property Loan Receivable, Maximum Exposure - This represents the maximum exposure to loss related to the Available for Sale Securities and Property Loan Receivables. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
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
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_DebtInstrumentAxis=ghi_GovernmentalIssuerLoanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |