Hubble has no thrusters, but it is large enough to have nontrivial gravity gradient and tidal forces acting on it. This would induce a torque that has to be cancelled by its reaction wheels. If I understand it correctly, this extra momentum, now stored in the wheels, would have to be dumped somehow. Does Hubble have any mechanism to do this on board? Alternatively, does it actually rely on the gravity gradient to dump momentum, rather than what I had assumed here? Does it actually need to dump momentum, and if not, why not?
Yes. It is done by magnetic torquers.
Magnetic torquer bars can provide control about the wheel-less axis, but they must also continue to dump momentum from the wheels to prevent wheel speed saturation.
Another good reference on the attitude control system is here.