The US singers updated the words to the tune, originally written in 1944, after a radio station banned it from playlists last year.
The original duet includes alternate lines between a man and a woman, where he tries to convince her not to risk a journey home in bad weather.
Instead, he says she should have another drink and spend the night with him.
According to Vanity Fair, Legend and Clarkson’s updated version includes the lines: “What will my friends think? (I think they should rejoice) / If I have one more drink? (It’s your body and your choice).”
During Good Morning Britain on Monday morning, Morgan accused Legend of being a “virtue signalling horror story” while discussing the lyrics with fellow host Susanna Reid.
Morgan said: “What is wrong with these people? John Legend, you virtue-signalling horror story and that dreadful wife of his, what’s her name? Chrissy Teigen.
“They’ve sat there plotting how to ruin a great Dean Martin classic just in time for Christmas.”
Reid, 48, asked why he believed Teigen had anything to do with it, before Morgan responded: “You don’t think she wrote these lyrics?
“She’s Miss Wokeville on Twitter. She’s got a hold of poor old Legend, who used to be great, and now he’s re-writing one of the classics of Christmas. Why? Why? Who wanted this re-written? What a load of nonsense.”
Reid urged for Morgan to leave Teigen out of the row, saying the only reason he had dragged her into it was due to previous altercations the duo have had.
Last year, Teigen waded into a row between Morgan, Little Mix and Ariana Grande after he accused the singers of “using sex to sell records”.
The US model tweeted: “Every time someone mentions Piers, his d*** gets another power boil and his nips cry tears of joy.”
Morgan accused Teigen of being a hypocrite and called her out for double standards.
The Standard Online has contacted representatives for Teigen for comment.