Being the pinion bearings,pinion bearing thrust pressure,incorrect pinion depth or improper set backlash. If all these are set correctly on a set of Ford or FRPP gears you should not hear noise. One of the simplest things to do is replace and people hardly do on gear changes and where the whine normally comes from inner pinion bearing. You can first try completely flushing your differential and refilling it before you replace everything. I used two bottles of Royal Purple 75W90 and one bottle of Ford Motorcraft friction modifier before. It often helps quiet down gear whine but other than that you'd probably have to get a new set of gears.Most reputable shops warranty their work and stand behind their work and should be willing to work with you on making it right. Also after you install new ring and pinion they must be heat cycled two or three times and be easy on your car for at least the first 350 miles. Differential fluid should be flushed and refilled after the first 500-600 miles and inspect and clean out any metal shavings/pieces found in the differential.