Refer to figures.
A spinning gyroscope retains its orientation relative to space and resists attempts to change its orientation, this is known as gyroscopic rigidity.  Changes in the orientation of a gyro's spin axis over time is called wander and there are two types:

Real Wander - This is the actual change in orientation caused by mechanical imperfections, friction etc.  All gyros will suffer from some form of real wander.

Apparent Wander - This is the apparent change in orientation seen by an observer on the Earth.  A gyro will maintain its orientation is space but an earthbound observer doesn't, as the Earth rotates the gyro orientation will appear to change when its actually the orientation of the observer that changes.

real wander in a gyro → INCORRECT.  Real wander is caused by mechanical imperfections and friction, the rotation of the Earth does not cause real wander.

precession in a gyro → INCORRECT.  A gyro precesses if an external force is applied, the reaction occurs at a 90 degree angle to the direction of spin.  Earth rotation does not cause precession of a gyro.

apparent wander in a gyro → CORRECT.  The rotation of the Eath causes apparent wander for earthbound observers.

a decrease in the rigidity of a gyro → INCORRECT.  Rigidity is reduced if speed of rotation or mass is reduced, Earth rotation has no effect.