HSBC Credit through Best Buy HSBC charged late fees on an account that was not late. Refused to remove charges. Internet

I have a Best Buy credit card through HSBC. My payment due date is the 28th of each month. I noticed that I had a late payment fee listed on my account, though I'd made a payment on 8/5. I called the company and spoke to a woman who first told me outright that my payment was late. I mentioned that I had two payments listed, one for 7/6 and one for 8/5, at which point she informed me that my cycle begins on the 6th of every month, so the payment I made just went to principle.

I asked for a manager and she told me that she could credit me $11 of that fee. I pressed and she said that she could credit 50% of the fee, $19. I insisted.

The supervisor she transfered me to was curt and impolite. She told me that I have no credit history with them so they would do no more than take off half of the late payment fee - in fact, that I have three payments with them and that one of those payments is late (despite being paid on the 5th?), so I'm in poor standing. She actually insisted in a rather accusatory tone that 33% of my payments are late. At which point I told her to just credit me the half.

The supervisor made it quite clear that this was my fault for not being aware of a date or policy that I was never informed of, and for not calling on the 5th to let them know that I was paying early. I looked through my statements and my email and I have no record of the 5th as the start of the cycle.

Cancelling the card. I have never been with a credit card company that ends the billing cycle ten days after payment is due. Nor was I satisfied with my customer service experience. The first woman was very polite and almost apologetic, but there is no excuse for that supervisor.