Tweed broke down in tears during the interview, as he recalled his final moments with Goody, who died of cervical cancer in 2009.
"Her whole body was moving because she was fighting to breathe," he said. "I couldn't sit there no more. I just kissed her and walked out. And it just went silent after a couple of minutes."
Former Big Brother star Hayes, who has been dating Tweed since 2010, later tweeted: "Just to clarify re. Jeremy Kyle interview today, I think Jack did very well and admire him for his commitment to Jade in the later part of her life.
"It is overwhelmingly clear to me we shouldn't have ever entered a relationship when he was still so badly grieving.
"This fact was never made clear to me and was always denied by him regardless of the support I offered to him.
"Lately, the toll of this has caused us to come to the decision that him staying with us when he is not yet ready to move on from the love of his life is simply unfair to all involved.
"Especially towards [her son] Blakely who deserves to have the world revolve around him until he knows better.
I would also ask certain catty magazines to respect there is a child involved and keep their comments professional.— Chanelle Hayes (@chanellejhayes) May 15, 2013
"I wish Jack all the best for the future and hope that he manages to learn to deal with his grief and be happy finally."
Hayes caused outrage last month when she tweeted that she was "f**king sick of living up to a ghost" after Tweed told a magazine how "no-one could replace" Goody.