Danny John Jules and Amy Dowden claimed to have a row that "made him cry."
The couple, who appeared that night, It Takes Two with Zoe Ball, once again appeared on the show to share the side of their story about angry arguments in training, where Amy "walked out crying."
MirrorOnline exclusively revealed that Amy, 27, cried when she called a producer on a BBC program after storming out of the studio where she and actor Danny, 58, had been practicing.
One source said: "Amy's call triggered panic, not least when she said she could not be paired with her again.
"They both have a few words and cross arguments throughout the series. But this is the biggest row.
"Danny is tired of all the training and he loses his composure. Amy thinks it's very bad. "
But tonight, the couple talked about the dispute, calling it a "loud voice in training."
Gethin Jones said to them: "This is a difficult week in training for Danny and Amy.
"There's been enough press about Strictly today and I know you want to say a few words about it. How do you want to respond?"
Amy replied: "Yes, this is our turn this time! Things have become rather intense the other day in training [Wednesday.]
"But do you know what we took half an hour to rest and go straight there.
"I never felt threatened or bothered by Danny. I really wanted to take this person to Blackpool, and then to the final."
Gethin then asks Danny what he wants to say, joking about them mentioning the round of the famous competition in Blackpool.
Danny replied: "Well, all I can say is the only reason I'm here, so far, is because Amy and I will never bite the hand that feeds me.
"I'm more than happy; maybe it's the best dance we've done in the last few days since I appeared on the show.
"And I'm happy to go, he's the boss, he's wearing pants."
Danny then jokes "not arguing with a Welsh woman," Gethin agreed.
After a bust-up, the BBC boss told Danny he must "be aware of his behavior moving forward" and spend the day convincing Amy.
The source was added to MirrorOnline: "They tried to put everything behind them.
"Danny is a perfectionist who strives to make every dance better and better. It's very common to warm up during training. "
While the Strict spokesman did not comment on the original story, a source said: "It was a difficult week for Danny and Amy but they returned to training and were looking forward to Saturday night."
Earlier on the show, Amy's former partner, Brian Conley, expressed his pride in Amy, avoiding the mention of recent arguments when he insisted that he would "get the best from him".
He said: "I love him a little but I am the first, and you never forget the first. But he comes in leaps and bounds and I am very proud of him."
Strictly Come Dancing will return on Saturday at 7pm on BBC1, while It Needes Two airs from Monday to Thursday at 18.30 on BBC2, and on Friday at 6:00 on BBC2.