My guess would be through the bank, since they issued the card and it is to them that you pay the bill.
I tried to pay fo the State tax software so I could file electronically, but always got stuck on the 'how to pay' page. Ultimately I printed the state return and sent via the USPS and filed the Federal separately, via e-filing with no issue. My guess is that TTax either has poorly designed software or doesn't want to make it easy to get an answer (I waited over 5 hours when I had a different question). I would dispute it through the bank because they wiull also have the initial payment.
