A characteristic called inductance makes some electrical devices behave like a flywheel; when current is flowing, it will want to keep flowing. Just as it takes torque to stop a flywheel, it takes voltage to stop current.
Some kinds of motors have significant inductance; if current is flowing from hot, through the motor, to neutral when the switch is opened on the power strip current will continue to flow from hot to neutral for at least a tiny fraction of a second. If there were no surge suppressor, the current would most likely arc through the switch. A surge protector with a voltage clamp between the hot and the grounding conductors, however, may offer a better current path. Current will go out the neutral wire of the motor, then the neutral wire of the power strip, the neutral return of the GFCI, and the neutral wire back to the panel. It will then travel through the grounding conductor wire back to the surge suppressor (bypassing the GFCI's sensing), through the clamping device, and back to the motor's hot wire.
A GFCI will trip if it sees current flow through the hot wire but not the neutral wire, or vice versa. In this scenario, the GFCI will see current in the neutral wire which didn't return through the hot wire, and thus recognize that as a situation where it should trip.
Some surge suppressors have one voltage clamp between the hot and grounding conductors, and between the neutral and grounding conductors, but none directly between the hot and neutral conductors. Getting a unit with a clamp between the hot and neutral wires may reduce false tripping, since the clamp between hot and neutral would offer a better path than the aforementioned one through the grounding lead, and that better path would not go through the neutral lead of the GFCI.