The BBC is to review whether "additional steps" should be taken when vetting guests for political debates.
The broadcaster was criticised over those given a chance to ask questions during its televised debate between candidates in the Tory leadership race.
It emerged that one guest had shared allegedly anti-Semitic tweets - he was later suspended from his job.
A BBC spokeswoman said "vetting and transparency" of guests for political programmes would be reviewed.
"We have a long history of producing successful debate programmes and this was no different," she said.
She said it would be "odd" to have members of the public as contributors who all agreed "with the politics of those they are questioning".
"We did however, adopt a different format for this programme and we will look at whether there are additional steps we might take on vetting and transparency should we repeat it in the future," she added.
On Wednesday after tweets by Imam Abdullah Patel came to light.
The BBC said Mr Patel re-activated a previously inactive Twitter profile in the aftermath of Tuesday's programme, Our Next Prime Minister.
The tweets had not been visible to its researchers before then, the BBC said.
A screenshot of Mr Patel's Twitter feed from 2014 posted on the Guido Fawkes website showed he shared a graphic of Israel's outline superimposed on a map of the US under the headline "Solution for Israel-Palestine conflict - relocate Israel into United States".
Labour MP Naz Shah was temporarily three years ago after it emerged she had shared the same image on Facebook.
Mr Patel would not have been selected for the programme if it had been "aware of the views he expressed", the broadcaster said.
Mr Patel, who asked the leadership candidates about the Islamophobic rhetoric faced by members of the Muslim community, was later suspended as deputy head of a girls' school.
Al-Ashraf primary school in Gloucester said it was investigating the allegations against Mr Patel.
Speaking to BBC Radio Gloucestershire on Wednesday, he said had not criticised the Jewish community, but stood by criticism of Israeli policy.
Separately, the BBC faced criticism on Wednesday for choosing as a guest on the programme a solicitor who has previously worked for Labour and once stood as a councillor for the party.
In response the BBC said the questioners "held a range of political views and we did not specify these views nor their backgrounds although some chose to do so themselves.
"The last questioner on the debate is a solicitor who was seconded by his law firm to the Labour Party in the past, rather than being a Labour 'staffer'. He is a Labour supporter and once stood as a councillor."