BBC News has not seen Millard’s resignation letter.
A Children in Need spokesman said: “Nothing is more important to us than the safety of all children and young people.
“When allegations were made in relation to LGBT Youth Scotland their grant was immediately suspended with the full support of the board and a review began. In order to do this thoroughly and fairly the review took three months and culminated in the decision to withdraw funding.”
Rennie, who had been chief executive of LGBTYS from 2003 to 2008 and is also a previous SNP adviser, was jailed in 2009 after being revealed as a member of a paedophile ring.
He was given a life sentence for sexually assaulting a three-month-old child and for conspiring to get access to children in order to abuse them. He was ordered to serve a minimum of 13 years, later reduced to eight on appeal.
Children in Need suspended grants to the charity in May 2024, after Millard says she alerted them to his case. It withdrew funding around three months later following a review.
However, Millard, who used to be an arts correspondent for BBC News, criticised Children in Need for what she said was a lack of due diligence.
She accused chief executive Simon Antrobus of failing to respond “with the necessary level of seriousness” and hesitating to take action.
She alleged that he eventually cut funding to the charity only because of fear of negative publicity.
BBC News has contacted Millard for comment.
Antrobus, who has been chief executive of Children In Need since 2016 and previously held senior positions at Parkinson’s UK and Scope, has not publicly commented.
Another man, who contributed to schools guidance put together by LGBT Youth Scotland, was convicted this year of sharing indecent images of children including some of newborn babies.
Andrew Easton was a young person who attended services of LGBT Youth Scotland in the 2000s, and, as a result, contributed to a 2010 guide for young people about coming out. However, he was never an employee of the charity.
He pleaded guilty in September to communicating online with someone he believed to be a child, downloading indecent images of children and distributing indecent images of children.
He was sentenced to a community order, ordered to carry out 200 hours of unpaid work, put on the sex offenders register for three years and told to take part in a sex offenders programme.
In 2022, two men said that they were groomed at LGBTYS around the time Rennie was chief executive. In response, LGBTYS suspended a staff member and referred itself to the police.
A Children in Need spokesman said: “The Children in Need board of trustees are supportive of the actions taken by the CEO and senior leadership team and stand by the decisions made.
“Rosie at all times retained the board’s support. In the wake of her resignation, in order to ensure any lessons learnt are captured, the trustees have instigated a review of ways of working between the board and executive in which Rosie has kindly agreed to participate.”
Mhairi Crawford, chief executive of LGBTYS, said that Millard’s resignation letter “demonstrates the ideologically driven nature of her attacks on our organisation”.
Crawford said: “We are pleased to see confirmation that Children in Need’s investigations into the work of LGBT Youth Scotland found nothing to report.
“Time and time again, those with anti-inclusivity motives point to historic allegations in attempts to destroy our reputation. Allegations that have been investigated and cleared by Police Scotland, and proven to have had no link to our work.”
Tim Davie, the BBC’s director general, praised Millard on Wednesday for her “significant impact on countless children”. Children in Need raised more than £39 million in its annual broadcast on Friday.