The journalist was a guest on Piers Morgan Uncensored, where he discussed Maitlis' comments about Dominic Cummings.
Raworth replaced Andrew Marr earlier this year.
Writing for the BBC, Maitlis said there are still unanswered questions remaining following the settlement.
The BBC said: 'We will be taking this up with Emily.'
The BBC broadcaster was told she had breached impartiality rules.
The BBC has published a list of news and political presenters who have earned money speaking at public events, in a bid to ensure impartiality.
The BBC newsreader retweeted a post by the 'Good Morning Britain' host criticising the government response to the coronavirus pandemic.
The broadcasting regulator is looking into the 'Newsnight' presenter's breach of impartiality after the BBC said it would not take action.
The Newsnight presenter didn't quite gauge just how monumental the content of the interview was at the time she was conducting it.
The BBC said the 'Newsnight' presenter's comments asked legitimate questions.
Fran Unsworth spoke during an online Royal Television Society event.
Maitlis took a night off from the programme after the broadcast.
The TV presenter said the PM's aide had broken the rules at the start of Tuesday night's broadcast.
A statement issued by the BBC said “our staff have been reminded of the guidelines”.
The 'Newsnight' presenter summed up the controversy surrounding the actions of Boris Johnson's senior aide with withering condemnation.
Edward Vines admitted in January to sending a letter to the BBC presenter via her mother twice.
Lord Hall said the BBC had to more carefully consider its role.
His previous appearance on the BBC was widely criticised.
The Duke of York's Newsnight interview at the weekend has been branded 'disastrous'.
We are all Emily Maitlis.