The corporation received multiple complaints who felt the joke was "inappropriate, and could incite violence".
The BBC panel show's team captain said critics believe they are “Momentum-inspired, lefty lunatics”.
The satirical panel show debuted on BBC Two on 28 September 1990.
The PM's chief advisor was the subject of a "pitch perfect" monologue from the journalist and broadcaster.
The Netflix series' creator hosted the BBC panel show on Friday.
Eamonn's recent comments about a coronavirus conspiracy theory have clearly not been forgotten by the BBC panel show.
"Go out in the garden, have a bit of sunshine, and stop believing complete rubbish," the Have I Got News For You panellist said.
This week's episode – which saw the panellists satirising the week's news from their own homes – got a mixed reception.
The topical BBC panel show has had to adapt due to social distancing rules.
Her top was a nod to Boris Johnson’s much derided insult to David Cameron.
Have I Got News For You descended into a tense row over Mercer's alleged links to a bust financial firm.
The footy host took the hot seat on Friday's 'Have I Got News For You'.
'Unless Ann Widdecombe has put off an entire gender, it's because they’ve said no.'
Host Jo Brand was praised for taking panellists to task over their comments.
An episode of Have I Got News For You where Jo Brand took an all-male panel to task over their jokes about sexual assault