The Britney Spears impersonator is said to have called the Risk member an "evil black b**tard" after he ordered her off a couch in the finalists' house.
Although the pair are said to be not speaking, Brucknell has apparently written a heartfelt letter to Mensah blaming the stress of the competition for her outburst.
"Kitty did not apologise face-to-face because Derry didn't want to speak to her for obvious reasons," a source told The Sun.
"In her letter, she said how sorry she was and that due to lack of sleep she might have said something offensive - but she wasn't sure because she was so tired. She told Derry she was really sorry for the argument and wants to be friends."
However, the insider added that Mensah is "not interested" in making up with Brucknell, despite attempts by the X Factor team to mend the situation.
"The producers gave her a firm talking to after the incident," they said. "They tried to get it resolved as soon as possible because she was very upset.
"Since then she's tried to be very friendly with Derry. But he's not interested. They used to talk and they got on well but she just snapped randomly."
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