Blockbuster Carrollton, Addison, TX Blockbuster has charged unauthorized late fee's to a credit card on file Carrollton Texas

I opened my credit card bill last month for a fairly new credit card (approx. 6 months old) and was surprised to find a charge for Blockbuster Video in an amount a little over $5. I called the store to find out how they could have charged my new credit card without my authorization, and I was told it was a charge for 'late fee's'. I asked since when a credit card number was taken and charged for late fee's that were not even more than a week late, and it hadn't been 2 weeks since, and was told it was 'in my contract' that they were entitled to charge the credit card on file when late fee's acrue.
For ONE: I can GUARANTEE that isn't in MY contract. I opened my Blockbuster account over 14 years ago, and didn't own a credit card.
I was told I needed a credit card on file only recently at this location in order to be able to rent certain video games for my son-in case they were not returned-understandably, but NEVER told that same card would be used for any movie late fee's. Late fee's are always either charged upon my next rental before I can rent, or billed to me in a paper bill since I first opened my account in the 90's. Never changed.
I told them I want this credit card removed from my account. There are times when I could be at my max, and a charge from them could put me over charging me an extra fee.
They said I couldn't not remove that number without closing my account.
I swore to not rent from that location again.
Today, I opened my new credit card bill for this month, and guess what? ANOTHER charge, this time for over $17!!! This time it says "Blockbuster, Addison TX", but since it's summer, and I have 5 children, I have been to this particular Addison location atleast every 3 days to rent a game or movie and if ever there's a late fee-I pay it right then and there. I was just there 3 days ago renting movies and a game and paid a $1 late fee I had at that time of rental, so how do they get $17...?!!!
This is clearly abuse of customers cards. I will now completely cancel my Blockbuster account if they will not remove this card. They could give a courtesy call, recording, paper bill if it's that significant for them to recoup the late fee's in less than 14 days!!!
I've seen many other reports of people's credit cards being billed without notice. This is nothing less than credit card fraud. I smell another class-action lawsuit.

Txcouple
Farmers Branch, Texas
U.S.A.