To replace the new reflector hold the bracket on the side of the handlebar opposite you with the flat pieces facing toward the front of the bike.

Spread the flat pieces apart and position the bracket so that the top flat piece will go over the top of the handlebar and the bottom piece will go underneath the handlebar.

Using light to moderate force, pull the bracket towards you so that it maneuvers around the bar. The bracket should now be reattached to the handlebar but spinning freely.