The comedian responded with a tweet of his own.
Raworth replaced Andrew Marr earlier this year.
The journalist stepped down as chairman of GB News this month.
The 72-year-old chairman of the new current affairs channel, who lives in France, is taking time off just two weeks after launching GB News.
Neil said he resented "even the thought that a channel of which I was chairman would peddle hate."
Michelle Dewsberry and Simon McCoy both read out rude sounding names live on-air during viewer phone-ins.
Comparisons have been made between the new channel and right-wing US channel Fox News.
The broadcaster will front the programme with Katty Kay.
Ex-Ipso chairman Sir Alan Moses said the organisation had to "be far more stringent in striking back at the attacks" made against it.
Zion Lights, spokesperson for Extinction Rebellion, told the BBC's Andrew Neil that "alarmist language works" when it comes to making people pay attention to climate change issues.
Long-running political discussion show This Week is to end following host Andrew Neil's decision to step down.