They will send your account to collections and it will screw up your credit.
"Apparently" there is a fee. Yes. And you were informed about it and agreed to it. All of the terms were disclosed to you and it's your own fault if you failed to read the information.
You aren't paying them for "nothing." The account is still open. They are still servicing it and generating statements, etc.
Put on your grown-up pants, pay the $20 and close the account. Or better yet, stay a stubborn self-entitled ignorant person and let them send you to collections. Your choice.
You have to pay them, this was all laid out in the contract you sign with the bank when you had your checking account with them. It will affect your credit report. Any bank checking on things 'outstanding' in your name will find it too.
You cannot get rid of them. You owe them to the bank pay them and be done with it
Take some responsibility, pay what you owe and properly close the account. That's what you agreed to when you opened it.
Oh, Tristan, you have a LOT to learn. People (and businesses) with access to technology and public records can really screw you over. And they enjoy doing it. Be smart, pay your bill.
What can they do to you? Pu it a a negative on your credit, which they WILL do or sue you for it, which they probably won't.