The Northern Ireland Affairs Committee claims the scheme should never have been established, despite former Prime Minister Tony Blair's insistence the "on-the-runs" letters, as they're known, were crucial to achieving peace.
The inquiry was prompted by the collapse in the prosecution of one of the recipients of the letters, John Downey for the 1982 Hyde Park bombing.
In 2013, the Old Bailey ruled that Downey's prosecution could not go ahead because he had believed that he was entitled to travel into NI and Britain from his Donegal home without fear of arrest because he had been told that he was not wanted.
The Police Service of Northern Ireland (PSNI) was blamed for what was described as a catastrophic mistake, while Unionists reacted with outrage saying the letters were unlawful and should be rescinded.
During the Northern Ireland Affairs Committee's public evidence sessions held in the Houses of Parliament, the Northern Ireland Affairs Committee questioned a number of serving and retired senior politicians including Mr Blair, who rejected claims that the letters were unlawful and said the scheme was essential for the success of the peace process.
However, committee chairman Laurence Robertson, MP, said the scheme had caused "further hurt to people who have suffered far too much already".
Peter Lynas, spokesman for Northern Ireland's Evangelical Alliance told Premier's News Hour that while he acknowledged the hurt the letters may have caused to victims of the Troubles and their families, he suggested it was also time for everybody involved to move on.
"They are part of our past now, and I'm not sure we're going to be able to do anything easily to undo them or un-pick them. Committees have looked at them, lawyers have looked at them, but it's difficult for the victims," said Mr Lynas.
Peter Lynas, spokesman, Northern Ireland Evangelical Alliance:
