If you know exactly where Marie and Thomas were married, I would start with trying to get a copy of their marriage certificate from that county, as very often the full names of the bride and grooms parents are included on the certificate. (I'm assuming you don't have that yet, as you say you don't know her maiden name.) Immigration records are frustrating- it's like looking for a needle in a haystack - so I've found it more fruitful to start with marriage and death certificates. I have managed to find quite a bit using both civil marriage registrations and catholic church records. Sometimes a death record will also list the parents as well.