The Commons Standards and Privileges Committee found the couple had been wrong to keep claiming parliamentary allowances even though they had only one habitable home.
But it said the rule breach was "significantly mitigated" because the arrangement was authorised by Commons officials, and they had not been trying to profit.
The committee said: "We conclude that Mr and Mrs Keen were in breach of the rules of the House because for a period of four months they claimed allowances for a second home when they only had one home available to them.
"This breach is significantly mitigated in our view by the approval given by the Department of Resources, by the lack of any evidence that Mr and Mrs Keen intended to procure for themselves a personal benefit, and by very difficult circumstances beyond their control."
Standards Commissioner John Lyon made clear that he regarded the breach of the rules as "serious", and involving "significant public funds". He suggested that Mr and Mrs Keen should pay back four months worth of their claims - some £5,678.
However, the committee of MPs took the unusual step of disagreeing with his findings and slashing the repayment, insisting that "in the exceptional circumstances of this case we take a more lenient view".
Renovations at the couple's home in Mrs Keen's constituency of Brentford and Isleworth, a short commute from parliament, started in May 2008.
However, following disputes with builders, the work stalled and the house was boarded up in December.
The MPs lived full-time in their Westminster property for the next 11 months, but continued to designate it as their second home and claim expenses.
The situation became public last June, when it emerged that the local council were threatening to repossess the property because it was derelict.
Within days the house was occupied by squatters protesting against the way the pair were getting taxpayers' money.
According to the report, Mr and Mrs Keen did ask the Commons Department of Resources for advice on the arrangement in May last year, and were told that the "exceptional circumstances" meant they were still entitled to allowances.
But Mr Lyon insisted 11 months was "too long" for them to have reasonably kept claiming.
"While this is a matter of judgment, my judgment is that by June 2009 they had been out of their Brentford home for too long for it to have continued to be considered their main home for allowance purposes.
"They had by then been out of the property for seven months and the work had yet to re-start.
"The arrival of the squatters was another serious setback, but by then the reasonable leeway had in my view run out."
He went on: "My conclusion is that Mr and Mrs Keen were in breach of the rules of the House in continuing to make claims on parliamentary expenditure for their central London flat when their home in Brentford was uninhabitable from June 2009 to October 2009.
"This was because, in my judgment, the rules require that a Member's home must be somewhere where they can stay overnight and that, having allowed a reasonable period for adjusting to the building problem that hit them late in 2008, Mr and Mrs Keen continued to be unable to stay overnight in their Brentford property during that period."
The commissioner said the couple had received a "personal financial benefit" from the accommodation arrangements between December 2008 and October 2009, and concluded that "some of the costs arising from their building problems were unnecessarily carried on parliamentary funds".
But the committee said the couple had endured a "catalogue of misfortune" and it would not be "fair to recommend repayment in full". Instead, it said the MPs should hand back £1,500 between them by the end of this parliament.
"While we would normally agree with the Commissioner on the seriousness of a misjudgment of this kind, in the exceptional circumstances of this case we take a more lenient view," the report said.
"Although, as the guidance makes very clear, Members are responsible for their own decisions, the express approval given on two occasions by the Department of Resources to Mr and Mrs Keen's continued claims for second home allowances when their main home was out of use is a very significant mitigating factor."
Campaign group the TaxPayers' Alliance pointed out that Feltham and Heston MP Mr Keen and his wife had not been asked to apologise, and called for the case to be referred to the police.
Spokesman Matthew Elliott said: "This is an appallingly light penalty for a serious and costly breach of the rules.
"Given the damning verdict on the Keens by the Parliamentary Standards Commissioner, the committee should have levied a far larger fine and demanded a full apology.
"This should not be the end of the matter, and the case should now be referred to the police for proper legal scrutiny."
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