if payment accepted with check

What is the name of your state (only U.S. law)? CA

I sent payment for a parking ticket on the day the ticket became passed due, paying the lesser amount.
I assumed the parking violations bureau would either give me a break for being 1 day late, and accept my payment, or send it back if they deemed the payment insufficient to cover my new late fees.
The check was cashed by them, so I assumed that settled the ticket. It turns out I now have a balance on the ticket for the late fee.
I though once a check was cashed , the person cashing the check agreed that the payment was settled.

Do I contest the amount owed because they cashed my check?
Thanks

You didn't pay the amount due so you owe the balance.

They would have cashed your check no matter what. You still owe a balance - you are better off taking care of the issue now and not let it go any further.

Next time I suggest sending the check in earlier or making the payment in person if you've waited until the due date.