The actor said they had got into an argument during rehearsals for Saturday’s Movie Week special.
However, speaking on Thursday’s This Morning, Caroline said she’s “going to learn to be quiet” after conceding she was in the wrong in the row.
Laughing, Caroline appeared surprised, saying: “It’s very nice of [him] to say that when we had our first barney yesterday.
“We’re both still slightly ‘ouchie’ from it, because I got a bit - OK, it’s quite hard sometimes to be told all the time by someone that is always genuinely right, it’s quite frustrating.
“I offered an opinion about a dance step, and I was entirely wrong but rather than back down gracefully, I just banged on about it.
“He just got really annoyed with me [laughs]. I was like, ‘Well I know I’m right about this’. And then about 10 minutes later I suddenly realised I was entirely wrong.”
Caroline admitted their “honeymoon period” is over, but she has learned her lesson when it comes to rehearsals.
She explained: “So, I think our honeymoon period’s over. I think it’s gonna be - no, actually, it won’t because I’m going to learn to be quiet.“
The pair will be performing their couple’s choice routine to Everything’s Coming Up Roses from Gypsy on Saturday’s movie special, which will also mark the first time there has not been a studio audience in Strictly’s 16-year history.
Earlier this week, it was announced the doors to the ballroom would be closed due to the second lockdown in England, with audiences not invited back until early December should they be permitted to do so under government guidance.
This Morning airs weekdays at 10am on ITV, while Strictly Come Dancing continues on Saturday at 7.25pm on BBC One.