When a magnet is moved close to a rubber band, the energy stored in the magnetic field does not change in a direct manner because the rubber band itself is not a magnetic material and does not significantly interact with the magnetic field. Thus, the correct response is:
The energy stored in the magnetic field does not change.
The rubber band may experience a force due to the magnetic field if it has magnetic properties, but in general, moving the magnet will not increase or decrease the energy in the magnetic field itself.