The planned performance has been compared to sexy 2000 film Coyote Ugly, with bosses deeming it unsuitable for prime time TV.
Cheryl, 35, and 28-year-old Oti have planned an impressive opening number alongside their fellow coach, 40-year-old Matthew Morrison, in honour of tomorrow night's semi-final show.
But it hasn't impressed the powers that be, with a source telling The Mirror: "Cheryl and Oti were wearing black outfits, but they whip them off to reveal scanty black leotards covered in 100,000 diamantes.
"The girls were throwing their legs around Matthew Morrison, who was gyrating his hips on stage.
"The producers worried it looked like they were recreating Coyote Ugly and they had to remind the choreographers it was a family show.
"They said it must be toned down before the live semi-final."
Noughties hit Coyote Ugly is famed for its provocative dance routines, with the film following a group of sexy barmaids who dance on stage in order to maximise their tips.
Tomorrow night's live show will see The Greatest Dancer's captains be joined by some of the stars of Strictly Come Dancing, including Neil and Katya Jones and Pasha Kovalev.
The inclusion of Strictly favourites left producers further panicked over the shock routine, as the BBC "pride themselves" on Strictly being "family friendly".
The insider added: "They can’t be involved in anything too raunchy.
"Producers want the opening number to be a spectacle and impress viewers but it can’t be too X-rated."
Cheryl has previously drawn Ofcom complaints for her provocative dance numbers during TV performances.
While promoting her comeback single, Love Made Me Do It, on The X Factor last year, the mother-of-one shocked fans by seductively licking her hand and grabbing her crotch during the show.
The routine received almost 100 complaints from stunned viewers, who also took to social media to criticise the performance.
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