I would at least mark both ends of the green wire with black or red tape as much as you can if it is indeed carrying a hot line. Not code, but at least it indicates the issue to the next guy. The green is probably being used because whatever that run was before was probably a 110V run, and that was converted to the second hot, or was done by an idiot. No bueno if so.... If there isn't a separate ground going to the sub panel then the GFCI is probably ineffective. Does the "test" button work on the GFCI? A single pole GFCI in a pool sub panel is usually used for 110V lights in the pool.
And for a pump you should have a dual pole 220V breaker somewhere but it could be in the panel that supplies the sub panel. They are expensive (like near $100) and many of electricians leave them off the pumps... If you have one upstream you are pretty safe even with that mess but it should be fixed eventually.