Labour finance spokesperson Joan Burton said internal documents reveal that Department of Finance officials were excluded from the final stages of negotiation over a deal.
A memorandum to government, which allows department officials express their opinion on major proposals before they are signed off, was also never issued.
Ms Burton said these measures were highly unusual and that the Oireachtas Committee on Finance intended to investigate the circumstances surrounding the deal.
"It's clear that in the rush to get a deal, normal governmental practices were bypassed. The exclusion of Department of Finance officials is deeply suspicious," she said.
Ms Burton said it was extraordinary that the final agreement, which was finalised by the Department of Education and the Attorney General, did not include a cap on expenditure.
Former Education Minister Michael Woods signed the deal, three days before he left office last June.
Only now are the full implications of the deal becoming apparent and some estimate the final bill for the scheme will top €1 billion.
This follows an unprecedented payout to a victim of child abuse believed to be between €300,000 and €400,000 on Tuesday.
This means Mr Wood's original estimate of a final bill of between €200m and €500m for the Residential Institutions Redress Scheme is very conservative.
Fine Gael education spokesperson Olwyn Enright said Education Minister Noel Dempsey should seek legal advice to see whether he can reopen the deal.
"The minister says he is happy with it, but the number of cases now coming to the Residential Redress Board and the level of compensation in this week's judgment raise serious questions about the way in which the Government has managed the issue," she said.
The terms of the deal see religious institutions paying out a total of €128m, while the State would be liable for all further compensation awards.
The actual cash paid over by the Church amounts to €40m, with the balance accounted by transfers of properties amounting to €35.5m. The Church is also providing counselling and other services worth €10m.
If the final bill to the State exceeds €1 billion, it means taxpayers will be paying 10 times more than the religious orders for decades of abuse.