Mr Adams appeared on the show to discuss the allegations of abuse levelled at his brother Liam, as well as the abuse suffered by his own siblings at the hands of their late father.
After this was discussed, Tubridy quizzed him on his involvement in the conflict in the North.
"Did you ever lose a night's sleep because of the activities of the IRA?" Tubridy asked him.
"I think that's a glib way to put it if I may say so," the Sinn Fein leader replied.
"Some people are watching tonight saying 'that man has blood on his hands', do you have blood on your hands?" Tubridy continued.
"No, I don't, and you might as well say that your grandfather had blood on his hands," Adams said.
"I was wondering were you going to bring that up, if you want to go glib Gerry, let's go glib," Tubridy replied.
Later in the interview, Adams told Tubridy the reason why he brought up his grandfather in the course of the interview.
"I wasn't being glib when I was talking about your grandfather, because you're obviously proud of your grandfather he was a member of the IRA, he opposed the treaty," Adams said.
Tubridy said that his grandfather had served with the IRA "in a very different time."
"I'd say if you looked into the audience, you could do a hands up and find at least a third of them had relatives that were in the old IRA."
"I don't think the comparison is remotely fair," a statement which drew applause.