I have a 4 wire cable leading to a pump in my lake. It has been a long time since I wired it, but I think the neutral(white) and ground are connected to the same point at the pump. I currently have it wired to a standard 20amp 240volt breaker. I recently tried to wire it to a 20amp 240volt gfi breaker, by wiring the white wire to the gfi neutral terminal and taking the pigtail from the breaker to the neutral bus. The breaker trips immediately. I suspect I should not use the white wire, just the ground wire, and still terminate the pigtail at the neutral bus. Also is this the same as wiring a 240volt hot tub. Thanks for your help

You won't use the neutral in this case, they wanted to get a better ground and put an unused wire to use, I don't believe you can parallel conductors, unless it is less than 50 Volts, or Larger than 1/0?
You can secure the unused neutral on the panels neutral bar.

From experience, there are some pump motors that will immediately trip a GFCI. Sump pumps are one type.

If a new pump trips a GFI, it needs to be returned.

When not wired through a GFI, they run fine. I seriously doubt that at least 20 new sump pumps over the last year were all bad.

What country were they made?