I'm slightly confused on the two prices. If you were quoted the lower price to do it then and they are asking for more now (for whatever reason) I'd pay the lower, original price in good faith.
Is it unprofessional to come back and ask like this? Slightly. It also strikes me as petty. They are chasing down $50 here and there? Must be a REALLY small company or they are REALLY hurting for cash. (or they had a biller that REALLY sucked and lost a LOT of money)
Here is how I would handle it:
First, email them so you can make sure its all in writing. No more "he said she said" later.
Agree to pay the original fee since that is what you originally accepted. Anything above that (for whatever reason) is on them.
When they agree to the lower fee, send a copy of the agreement with a money order for the amount paid to the company name in case its an employee trying to squeeze some personal $$ out of customers. (boss forgot to charge them so I'll call and collect/pocket the difference)
Sending a money order also protects you from them hitting you for the larger amount instead of what you agreed to.