If the customer received their funds back through the chargeback process then you need to record that manually in ThinkReservations to update the reservation. It also ensures that your staff doesn't accidentally refund.
Update the reservation
To update a bill or reservation that had a chargeback, follow the steps below:
Open the reservation or bill in question.
Click one of the green Payment buttons.
Update the amount to be adjusted. Put a dash or hyphen in front of the amount to show it's in the negative.
Change the payment type to Third Party Credit Card Processor.
Enter a note in the Reference Number box, such as "chargeback".
Optional: Update the payment date to when the payment should be, if not today.
Click Take Payment
This payment will update the bill to reflect that funds have been removed for the specified amount, date, and note.
If you later win the dispute, you can delete the payment, since it's only a journal entry, provided a Night Audit hasn't been run to lock the books. In that case, you can add another payment the same way, but in the positive to reflect the funds being added back into your account.