Someone is telling you fibs.
The diff case side cover is sealed with an O ring seal. The diff side cover is held in place with 7 bolts (those threaded studs sticking out aren't correct), and likely the cause of the issue.
It should be possible to remove the side cover with the diff in situ, so the O ring seal can replaced, once the drive shaft is pulled from the diff (suspension needs unbolting to allow this).
However as the diff is a reconditioned (and badly by the looks of it), I'd check those threaded fixings are pulling the casing together correctly, before doing any further work.