The presenter sparked controversy after he asked why the royal family wouldn’t "just throw him over the balcony and her with him".
After 15 years, the GB News anchor stepped down as a host on This Morning in December.
"This isn’t a version of events that we recognise."
The presenter has insisted he didn’t have “any issues” with the shake-up, but was not happy about the way the matter was handled.
The presenter compared Ruth to Nurse Ratchett from One Flew Over The Cuckoo's Nest.
Eamonn Holmes Breaks Silence On This Morning Exit And Claims He Hasn't Yet Heard From Phillip And Holly
"Put it this way, I’m looking forward to a move somewhere new where they’re pleased to have me," he said of his new GB News role.
Last year saw Eamonn's regular Friday slot on the ITV show given to Dermot O'Leary and Alison Hammond.
Eamonn Holmes Admits Telling Anne Robinson He'd 'Knock Her Head Off' If She Were A Man After Parenting Jibe
The This Morning presenter recalled being furious after the Countdown star made a dig about him “sacrificing fatherhood for fame".
The presenter said he was "absolutely gutted" to miss the show.
"It has opened the door to a conversation that I feel needs to be had.”