Using a 120v relay in this configuration is not recommended and could cause unsafe conditions. This setup intentionally creates a ground fault where current runs through the safety ground instead of the normal return path. . Using a 4 wire 240 setup and powering the relay with a Neutral would eliminate the safety issues, however care must be taken to ensure the station is not used on a 208v or single phase 220 - 240v circuit. The best solution would be to replace the 120v coil relay with a 208 - 240v AC coil model such as the Packard C240C.
Running the relay coil wire through the GFCI coil will allow the station to operate by faking out the sensor so the ground fault is no longer detected.