That bushing is called the pinion snubber. It's really only there to prevent the differential from hitting the chassis when the shocks bottom out. If the car is clicking from the passenger side I would look at the upper control arm, lower control arm, quad shock, and the main shock on that side. Check to make sure bone of them are loose and the bushings aren't worn out.
Sold - Black 2000 Mustang GT, gone but definitely not forgotten
- Silver 2007 Corvette
Current - DHG 2001 Bullitt