Professional dancer Du Beke recently made a public apology for describing his celebrity partner Laila Rouass as a "P**i" in training.
Anti-racism groups have since called for Du Beke to be dropped from the programme. Dozens of fans have also complained about the incident, which was not broadcast.
However, a BBC insider told The Mirror: "It's done and dusted now, and a line has been drawn under the whole matter. Laila has forgiven Anton and that's what really matters.
"He is utterly mortified and realises it was a totally unacceptable thing to say. But it has been put down to silly banter that went too far. Anton has offered a full apology and they are both happy to leave it at that."
Rouass has stated that she accepts Du Beke's apology and wants to concentrate on progressing further in the BBC One contest.