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Accounts Payable, Accrued Expenses and Other Liabilities - Additional Information (Details) - USD ($) | 1 Months Ended | 12 Months Ended
--- | --- | ---
Dec. 31, 2022 | Dec. 31, 2022 | Dec. 31, 2021
Lessee Lease Description [Line Items] |  |  |
Deferred gain on sale of property | $ 6,596,622 | $ 6,596,622 |
The 50/50 MF Property [Member] |  |  |
Lessee Lease Description [Line Items] |  |  |
Initial lease term expiration period |  | 2048-03 |
Expenses related to the agreement |  | $ 162,000 | $ 168,000
Ownership interest sold | 100.00% |  |
Deferred gain on sale of property | $ 6,600,000 | $ 6,600,000 |

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- Definition Initial lease term expiration period. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | xbrli:gYearMonthItemType
Balance Type: | na
Period Type: | duration

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- Definition Sale of real estate ownership interest percentage. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | dtr-types:percentItemType
Balance Type: | na
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- Definition Amount of gain on the sale of property that does not qualify for gain recognition as of the balance sheet date. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
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
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
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- Definition Amount of operating lease expense. Excludes sublease income. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 842 -SubTopic 20 -Section 45 -Paragraph 4 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918638-209977 + Details
Name: | us-gaap_OperatingLeaseExpense
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Details
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