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Breaker size is based on the motor HP and wire size attached along with the operating voltage .
Can you check the setup and post for the proper determination?
The existing breaker should have the size imprinted on the breaker handle also.
It is rare for a GFCI to burn out, were there any other indications of problems prior to the issue?
Let me know and we can continue
It should not affect the breaker, if the breaker is sized properly with the correct wire.
Still need the motor horsepower and if the breaker is a single pole or double pole to size the breaker.
Check the wire size at the same time and we can be sure the wire is correct for the breaker.