When a magnet is moved close to a rubber band, there is no direct interaction that would change the energy stored in the magnetic field itself. The rubber band is generally not a magnetic material, so it wouldn't create or modify a significant magnetic field.
Since the question is about the energy stored in the magnetic field, the best answer from the options provided is:
The energy stored in the magnetic field does not change.
This reflects the fact that the presence of the rubber band does not influence the magnetic field's energy directly.