To edit what type of payments you want to accept you will need to navigate to your POS > Go to the Manager page > Configuration > Tax/Tender/Cash > Tender.
At the bottom of the screen you will see the option for "Available Online". These are the settings that will determine what type of tender types you will accept in Thrive Online.
If you do NOT want a specific tender type accepted, uncheck the box. For example, if you want to require online customers to pay with a credit card, you would uncheck the Cash box for "available online"
Be sure to save your changes. If your system is set to update Thrive Online automatically, you will see a message "Sending to TOL". If not, you will need to navigate back to Thrive Online and perform an import to make sure your changes come over.