The Board also noted it also defended expelled member Tony Greenstein and Chris Williamson, who was then a suspended MP.
In February, Mr McDonnell attended the LRC conference, where he listened sympathetically to a discussion on the case of Jackie Walker - the Labour activist who claimed to be the victim of a "political lynching" when she was suspended over her comments about Holocaust Memorial Day and Jews' role in the slave trade.
At the conference, Mr McDonnell said he would "take up" her case with Jeremy Corbyn and General Secretary Jennie Formby. Ms Walker was later expelled from Labour.
On Sunday, Mr Marr asked Mr McDonnell if he felt his party's antisemitism crisis had hurt Labour at this election.
"I worry that this has had an effect," Mr McDonell said. "We've done everything I think we can possible do. We've apologised to the Jewish community."