Britain's first minister for children agreed to pay pound;10,000 to a charity and to cover Demetrious Panton's legal fees of at least pound;10,000, after he threatened libel action over her remarks.
Mr Panton, now a government adviser, was abused while in the care of Islington council in the 1970s. He tried to alert Mrs Hodge to the scandal between 1982 and 1992, when she was council leader.
Teachers' leaders said this week that her credibility had been irreparably damaged by the incident but Tony Blair stood by his former Islington neighbour.
The payments to Nacro (the National Association for the Care and Resettlement of Offenders) and Mr Panton are unlikely to cause a major dent in her bank balance. Mrs Hodge is worth an estimated pound;8.9 million and receives an annual dividend of pound;101,890 from her shares on top of her pound;93,403 salary as a minister.
The latest row surrounding the controversial MP for Barking erupted after Mrs Hodge urged Gavyn Davies, BBC chairman, to block a Radio 4 programme carrying claims that Mr Panton had attempted to contact her in 1985.
Mr Panton, 36, was appalled that she had described him in a letter to Mr Davies as "extremely disturbed" and was unhappy with her private apology.
Since her appointment as minister for children this year, Mrs Hodge has faced repeated calls for her resignation over claims she had failed to do enough to tackle the Islington paedophile scandal. But Michael Foster, her parliamentary private secretary, said she had no plans to step down.
Mrs Hodge is part of a select team of Labour women MPs - along with Harriet Harman and Tessa Jowell - who she refers to as "The Volupts". (She told The Daily Telegraph they were "women of a certain age who've forgotten what colour our natural hair is, but we're voluptuous.") The 58-year-old has benefited from the support of Tony Blair, who lived in the same Georgian crescent in Islington as Mrs Hodge before he became Prime Minister.
Tony Blair this week told the House of Commons that Mrs Hodge had done an excellent job and had answered the claims properly, criticising the Conservatives for launching a "wholly unfair campaign to oust her".
Michael Howard, Tory leader, retaliated by questioning the suitability of someone who had "bullied her way out of trouble".
He said the Prime Minister had lost all sense of shame. "You may care about vulnerable ministers, we care about vulnerable children," he said.
The National Union of Teachers backed calls for Mrs Hodge's dismissal.
Doug McAvoy, NUT general secretary, said: "She is a holed vessel and she should be sacked.
"There is no precedent for a minister of the crown to have to make that kind of apology and still cling on to their job.
"If the Government is serious in its approach to child protection the person who should be bringing those changes about should be above question.
Nobody but nobody could say that about Mrs Hodge."
A LITANY OF HOWLERS
October 1992 Accuses the London Evening Standard of a "sensationalist piece of gutter journalism" after it reports that young people in care homes in Islington were being lured into sex, drugs and prostitution. The newspaper is proved right and Mrs Hodge is forced to admit the council had failed.
February 1999 Says that Ken Livingstone should not become mayor of London because "he was more interested in twinning with Nicaragua or inviting Sinn Fein over" when he was leader of the Greater London Council. Neglects to mention that when she was leader of Islington Council the red flag flew from the town hall and a bust of Lenin was placed in the lobby.
May 2002 Refers to university students as "customers" and says she does not see why "the state should pay for students to go and drink beer". In response, the London Student newspaper set up a website called Hodgewatch.co.uk demanding she improve her work.
March 2003 While on an official trip to China, she pledges to "set a target on closing the gap" between the number of private-school and working-class teenagers who win places on degree courses. She is swiftly made to retract by Charles Clarke.
November 2003 Describes a child-abuse victim as "extremely disturbed" in a letter to the BBC, urging them to block the broadcast of his claims. She is forced to apologise and make a donation to charity.