I guess you've opened yours. I have yet to see the inside of one of those. Could you post some pictures? It may help getting you some answers.
That being said, let's speculate!
High power GFCI do not have built-in contactors (unlike the 120V GFCI outlets commonly used in houses). Maybe this is the control signal that energizes a contactor located on the main board. I'm currently building my own EVSE as a learning exercise. Its overall design is very similar to the MC240: compact and portable. In the design phase, I quickly came to the conclusion that by using a secondary small relay located along the GFCI sensor control wire on its way to the main contactor, I only needed one contactor. The relay is controlled by the J1772 state machine, running in a micro-controller.
A further refinement would be to replace the off the shelf GFCI sensor by a coil and an amplifier, feeding its signal into the micro-controller. This would save the need for a second relay and significantly reduce the size of the EVSE...