The remaining panel members, including Lynda Bellingham, Carol McGiffin, Andrea McLean and Lisa Maxwell, are "furious" that producers didn't consult them about the pair's replacements and have threatened to reduce the number of days they work unless they're given more say, the Sunday Mirror reports.
Carol Vorderman and former Coronation Street actress Sally Lindsay will apparently replace the axed duo and are expected to sign contracts for the ITV1 show next week.
"All the girls were pretty peeved about the way in which Kate and Zoe were handed their notice," a studio source said. "The women are, and were, a tight-knit bunch. They didn't feel change needed to be made in such a dramatic fashion.
"To rub salt into the wound, they actually read about it in The Mirror before being told by execs.
"There is some concern that, because they didn't all screen-test together, the chemistry will not be completely right. Things are tense at the moment as no-one feels their job is safe."
An ITV source added that the changes were made to keep the lunchtime panel show "fresh and exciting".
Tyler recently described her axe from Loose Women as "sudden" and "a bit of a shock".