What cancels the permit for use of a motorized bicycle?

Your answer is correct because both "clearing out" the silencer and modifying the gear ratio change the motorized bicycle's technical specifications in a way that exceeds legal limits for this vehicle category. According to German traffic regulations, these modifications can increase speed or noise beyond permitted levels, which cancels the permit for use of the motorized bicycle. Installing a second rear-view mirror, however, does not affect the vehicle's performance or legal classification, so it does not cancel the permit. Remember, any modification that alters speed or power beyond the approved design can invalidate your permit.