The former Prime Minister's daughter was dropped from the programme after referring to a black tennis player as a "golliwog" in the backstage green room. Her agent Ali Gunn later urged producers to apologise for leaking a private conversation.
The BBC has received more than 2,200 complaints over the decision, as well as 60 calls and emails backing the move.
BBC One controller Jay Hunt defended the corporation's actions, saying that Thatcher had been given "ample time to apologise".
"What Carol decides to say in the privacy of her own home or in a private conversation with friends is one thing," she told Radio 4's Today programme.
"What she says in a green room space, when there are 12 people, in her capacity as a roving reporter for The One Show is a rather different thing."
Hunt claimed that Thatcher's comments were "deemed by a very substantial proportion of the public to be hugely offensive".
She added: "What I find sad about the entire situation is that we have given Carol ample opportunity to apologise for offence that was caused to key named individuals."
Thatcher, who won I'm A Celebrity, Get Me Out Of Here! in 2005, has only been dropped from The One Show and not the BBC as a whole.