Backlash between the ring and pinion can be adjusted by shims. The time consuming part is to determine which has to move, the pinion or the ring gear. If it is the pinion due to being too deep or too shallow on the ring gear then you will have to remove the pinion, press the inner bearing off and add or remove shims. Then press the bearing back on, reassemble and recheck backlash. When moving the pinion after looking at a gear pattern and determining if you are close or not I like to make major changes in the approx. .010" range and minor adjustments around .003"-.005".
If you determine that the pinion depth is correct and only need to move the ring gear that is much easier as you simply move shims from one side of the carrier to the other. I like to measure total shim thickness and write this number down prior to messing with shims. I do this so that the carrier preload will be the same once the installation/repair has been completed. If you take .010" from the left side of the carrier make certain to add .010" to the right side. This keeps the same preload on the carrier side bearings.