Most times the pinion shim can be reused but only if the new crush sleeve is pressed to the spec of pinion gear rotating torque. The side shims can usually be reused too but when the entire differential and new gears are installed, many times adjustments are needed. GM has a special tool that allows one to measure pinion depth and with some math, figure out the proper pinion shim. From there, all one has to due is crush the sleeve to the proper rotating torque, set the diff in with original thickness shims (although GM wants the cast iron "spacer" removed from each side and replaced with appropriate thickness steel shims, and measure pattern. GM actually makes two or three different measuring tools for picking side shim thickness too but it moves with new parts even less than pinion shim thickness. Aftermarket gears usually have the pinion depth required etched into the rear end of the pinion gear.

To make a long story short, you don't actually need to adjust the pinion alone....it needs to have the pattern run and reset....which should include another crush sleeve, possible pinion shim change, and possible side shim change.....or any combination thereof.