Labour wants the Oireachtas Education Committee to hold hearings into the 2002 indemnity deal between religious congregations and the State in relation to compensating victims of child sex abuse.
The deal saw religious orders and the State agree to split the cost on a 50-50 basis - but the actual redress bill has seen the congregations' share fall to as little as 13%.
Education spokesperson Joan Burton believes a committee of investigation into the deal would be worthwhile.
"We had for instance a couple of years ago, a relatively successful Dáil inquiry into what happened in terms of the banks," she said.
"This again is a very large significant amount of money and I think as a society and as a parliament we are entitled to know, how was this endemnity created, who signed off on it, we know there are conflicting versions of responsibilities."