I want to dispute a charge on a check despite my date's objections
Do you still have the check?
It must be somewhere, just give it back to me or I will give you my signature
It is ok to have minor disagreements like this in a relationship. But if the charge is reasonable, it might be better to just respect your girlfriend's wishes and not create extra conflict over it.
What if I refuse to pay her back the money from the check?
If you are taking your girlfriend out on a date, you should not be expecting her to pay for half of the bill. This is a time for you to be generous with her, to let her know that she is valued.