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v3.23.1

Secured Line of Credit - Summary of Secured Line of Credit (Parenthetical) (Details) - Secured Line Of Credit Facility [Member] | 3 Months Ended | 12 Months Ended
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Mar. 31, 2023 USD ($) Extension | Dec. 31, 2022 USD ($) Extension
Bank United General [Member] |  |
Line of Credit Facility [Line Items] |  |
Debt instrument number of extensions | 2 | 2
Debt instrument extended maturity period | 1 year | 1 year
Payment of extension fee percentage | 0.25% | 0.25%
Bank United General [Member] | LIBOR [Member] |  |
Line of Credit Facility [Line Items] |  |
Debt instrument variable rate | 3.25% | 3.25%
Floor rate | 3.50% | 3.50%
Bankers Trust Acquisition [Member] |  |
Line of Credit Facility [Line Items] |  |
Debt instrument number of extensions | 2 | 2
Debt instrument extended maturity period | 1 year | 1 year
Payment of extension fee | $ | $ 25,000 | $ 25,000
Bankers Trust Acquisition [Member] | SOFR [Member] |  |
Line of Credit Facility [Line Items] |  |
Debt instrument variable rate | 2.50% | 2.50%

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- Definition Debt Instrument extended maturity periods. + References No definition available. + Details
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Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

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- Definition Debt instrument number of extensions. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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- Definition Debt instrument payment of extension fee. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Debt instrument payment of extension fee percentage. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

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- Definition Floor interest rate. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | instant

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- Definition Percentage points added to the reference rate to compute the variable rate on the debt instrument. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
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Balance Type: | na
Period Type: | duration

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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_CreditFacilityAxis=ghi_BankUnitedGeneralMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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

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

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