The gfi is tripping because it is measuring a very small imbalance in the current between the hot side of the circuit and the neutral side of the circuit.
I'd open up the smoke generator and check the wiring for insulation wear.
Some questions. Does the gfi trip when the puck feeder cycles, or does it trip when the puck burner is heating up? If it only trips when the puck feeder cycles, I'd suspect that the arm between the motor and the shuttle has rubbed against a wire and worn through the insulation. If the shuttle operation doesn't affect the gfi, I'd look carefully at the wiring to the puck burner. If I still didn't see anything, I'd look carefully at the rest of the wiring in the smoker generator.
It is also possible that the gfi was damaged by your recent lighting storm. If you can't find a problem with the smoke generator, I'd replace the gfi and see if the problem goes away.
