Derry, 21, from boyband The Risk, complained to show bosses after the pair got into an argument, saying he thought Kitty, 26, called him an "evil black b******".
A source said: "She apologised for the argument. But she has denied calling him anything. The matter has been investigated and it's been resolved."
The pair sat down to lunch together on Tuesday and the source said that they appeared to be getting along well.
Kitty, mentored by Louis Walsh, has always denied the claim.
An X Factor spokeswoman said: "There was an argument between two contestants which was looked into by production and the matter has been resolved."
Kitty has divided viewers of the hit ITV1 talent show with her over the top performances and outrageous costumes and last week admitted that she would not "win a popularity contest".
This weekend's show is expected to see Kelly Rowland, who has been involved in a row with rival judge Tulisa Contostavlos, return after she dropped out last weekend due to illness.