You should enquire at the Dept of Social and Family Affairs or at your local Citizens Information Service.
Most people who have paid PRSI (or a "stamp") for at least some of their working lives will have an automatic entitlement to a fixed contributory pension (i.e. based on their PRSI contributions). If this is your father, he would automatically be entitled to an allowance in respect of your mother and she, in trn, would have an automatic entitlement to a widow's pension should anything happen your father, even though she may never have paid PRSI herself.
If neither parent has ever paid enough PRSI to qualify automatically, either or both may still be entiled to a non-contributory pension. For this, they would have to undergo a means test and disclose detais of personal savings, assets and income from other sources (such as the US pension). Depending on the extent of these, their maximum entitlement may be reduced, potentialy to zero.
Bottom line is that they've nothing to lose by applying.