There are different parts to a contract;
Offer
Acceptance
Consideration.
They offered the money, you accepted their money and the money (the consideration) was exchanged. You also accepted the 'terms', if you hadn't, you'd never have received the money.
You are on a sticky-wicket if you are trying to wriggle out of your obligations due to an administrative oversight.
You may find it far more costly in your attempts to get out of this contract, than simply to pay what you owe.