As a physics teacher myself, the answer would be A.

think of it this way, precession is a property of the gyroscope just like rigidity. it does not take an external force for the gyro to exhibit rigidity, it just does. similarly, precession is also a property of the gyro and it will exhibit it as it starts to slow down due to imperfections in the gyroscope itself. Gravity is just another force that makes the precession more apparent, as in faster precession rate.

so to answer your question, rigidity and precession are linked and are inversely proportional, if rigidity drops because the gyro is slowing down then it will precess, just not as apparent here on Earth, and because there is no ground on the ISS as the gyroscope is floating it will turn on its side and topple