Even the judo champion involved, Cynthia Rahming, was left bemused. "I wasn't offended - I didn't find it sexist," she told The Mail on Sunday.
Elsewhere, it divided opinion, with some TV presenters, including Mariella Frostrup, 51, backing the BBC's stance.
She said: "'Girls' to me is a fantastic word because I think, "Girls... full of potential." But it has been used as a dismissive term as well. So I can imagine why it would be controversial. The athlete may not have been offended but the BBC has to think of the sensibilities of everybody watching."
Feminist novelist Kathy Lette, 55, however, said: "If the athlete didn't find it upsetting why should the BBC mount their politically correct high horse and gallop off into the sanctimonious sunset?"
The row comes two weeks after the Corporation was accused of double standards after it forced veteran broadcaster David Lowe to quit for mistakenly playing an old version of The Sun Has Got His Hat On, which featured the N-word. Jeremy Clarkson, however, kept his job, when he appeared to use the same racist term during the filming of Top Gear.
It also follows the BBC's decision to replace John Inverdale with Clare Balding as its Wimbledon presenter on 5 Live following his sexist comments about Women's Champion Marion Bartoli last year, and the criticism of the Premier League for not sacking its chief executive Richard Scudamore over emails he sent containing derogatory jokes about women.
The Queen's Baton Relay charts the progress of the baton as it tours Commonwealth countries ahead of the Games in Glasgow in July. Mr Beaumont, a record-breaking cyclist, interviews athletes during the journey. A BBC spokeswoman said because the baton's tour was treated as a news event, the unedited version of the documentary was broadcast soon after being filmed.
"They had more time to edit it the second time," she added. "Mark didn't mean to cause offence. But the word 'girl' was taken out just in case it did."
Before its first airing, the programme was seen by a lawyer and an executive to ensure it did not breach BBC guidelines. The uncensored clip remains on the BBC's website.
In the clip from the documentary, shot in the Bahamas, Beaumont interviews D'Arcy Rahming, the head of the Bahamanian Judo Association, before being given a demonstration by his daughter, Cynthia, who is due to represent her country in the Games.
Within seconds the presenter ends up flat on his back. After his comment about being beaten by a girl, he adds: "You should be good - you're going to the Commonwealth Games."
Beaumont was unavailable for comment yesterday.
Former TV presenter Anthea Turner, 53, said: "It's mad. I think people have got to stand back, stop all this. It is just silly... We have got to be able to have a sense of humour. I feel that there are certain issues you really have to be sensitive about, like race, but you must be able to have a laugh about something. The problem now is that people have become over-sensitive - and the BBC has become too over-cautious."
But Miriam O'Reilly, 57, who sued the BBC for age discrimination after being dropped as presenter of Countryfile, took a different view.
She said: "The response from Mark Beaumont to Cynthia Rahming throwing him to the ground was to emphasise his faux embarrassment. He used the word "girl" because it has connotations of being younger and weaker. I think he immediately realised what he said was sexist.
"He knew he was going to be thrown by Cynthia, she is a first-class sportswoman at the top of her game. He and the director obviously thought to play up the being thrown by a "girl" aspect would be funny, when in reality it's an example of casual everyday sexism."
- Mail On Sunday
