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McGuinness took over from previous host Sue Baker, who had held the role for 24 years, back in September - alongside new team captains Olympic gold medallist Sam Quek and former England rugby star Ugo Monye, who took over from Phil Tufnell and Matt Dawson.
After it first aired, the new-look version of the show received mixed reviews, with some viewers calling on the BBC to bring back the original line-up.
And it seems as though among those who aren't too keen on the show is Clarkson, who took to Twitter to give his verdict.
The 61-year-old wrote: "What on earth has happened to Question of Sport?"
But McGuinness quickly responded with a cheeky dig at Clarkson, replying: "The same thing that's happened to Top Gear JC. New personnel, bigger ratings. Love you."
He ended his tweet with a kissing face emoji.
The same thing that's happened to Top Gear JC. New personnel, bigger ratings. Love you :kissing_heart:- Paddy McGuinness :blue_heart: (@PaddyMcGuinness) October 15, 2021
Clarkson is yet to respond to McGuinness's tweet, but in a follow up he wrote: "I only watched it for 10 minutes and I have a terrible headache. Why can't they all calm down?"
Clarkson left Top Gear in 2015, with McGuinness taking over hosting duties in 2018.
McGuinness has previously said it was a 'privilege' to host Question of Sport.
I only watched it for 10 minutes and I have a terrible headache. Why can't they all calm down?- Jeremy Clarkson (@JeremyClarkson) October 15, 2021
He kicked off the first episode by telling viewers: "Hello and welcome to a brand new series of Question of Sport.
"I've got to say, what a privilege it is to be sitting in this chair.
"I'm going to be asking the questions and two new team captains will be giving me the answers.
"Well, hopefully or things might get a bit awkward.
"One is an Olympic hockey gold medallist and the other a Lions and England rugby star.
"Please welcome, Sam Quek and Ugo Monye."
But some viewers were a bit disappointed with the show's new look and took to social media to vent.
Posting on Twitter one person wrote: "Well done BBC, you've completely ruined Question of Sport. A real shame."
Another said: "I really don't like this new Question of Sport. I miss Tuffers, Daws and Sue."
While a third added: "Why change a winning formal - bring back Sue Barker, Tuffers and Matt. It's just not as much fun!"