The mathematician was joined on BBC Radio Wales alongside her co-host Owain Wyn Evans and guest Judge Rinder.
Carol explained that she took issue with her pal – who she jokinlg refers to as her fiancé – after he chose Susanna to take part in the Channel 4 show.
It comes as the mum-of-two revealed she called the GMB presenter as soon as she was made aware of Susanna’s debut on Celebrity Gogglebox.
Carol mused: “Will you stay on the line… I’ve got a bone to pick with you fiancé about Gogglebox.
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“Given the fact that I’ve given you my heart and given you my soul… WHY, last year did you ask Susanna [Reid] to do Gogglebox with you and not me?”
Judge Rinder replied: “I think that’s how it works on TV. You know television people, they sort of phone you up and give you a range of options of who you want to put in your house.”
He went on to explain that the show producers had suggested Susanna and he took them up on their offer.
Judge Rinder added that he and Carol would be a “disaster” together on-screen.
Carol remarked: “Anyway, my dear, darling fiancé… I rang Susanna [Reid] as soon as the trailer run.
“I said, ‘What’s this with you and Rob?’ And she said, ‘Oh, well I’ve been asked.'”
She continued: “So I told her, ‘Mud wrestling as soon as lockdown is over. I’m going to mud wrestle you Susanna [Reid] for Rob’s hand.’
Carol added: “We’ll be mud wrestling over you.”
Judge Rinder initially warned the BBC Wales host against the idea but suggested he would have to referee the match.
Carol went on: “I’ll provide the paddling pool and it’s going to happen in your back garden this year Rob. I’ve already told Susanna.
“She’s not as for it as I am, obviously.”
The cheeky back and forth comes after Judge Rinder and Susanna, who have been friends for more than six years, appeared on Celebrity Gogglebox.
Carol, who is also friends with Susanna, is the longtime pal of Judge Rinder also.