Hot Tub ... uses straight 240 V, no neutral.
I mistakenly installed 6-3 w/#10G, do I attach the neutral up anyway even thought the neutral isn't connected at the hottub?
I didn't see where anyone tackled this question, yet.
If you left it white and hooked it to the GFCI, any current that ever travels on it would not trip the GFCI.
If the GFCI protection relies for this equipment on there being no neutral current, then I would not hook the white wire to the neutral on the CB.
I say green tape the white wire at both ends and use it for an extra ground.
I see a plus to using this for extra fault current on a 240 V hot tub.
Call it the back up grounding conductor as if you intended it that way all along.
Having a #6 ground makes sense since I infer that this tub has a 50 A CB and is distinctly a wet and barefoot location.
As for the white pigtail on the CB itself, I would hook it to the neutral bar even though it technically carries nothing. That's probably the only way it is intended to be installed.