No rust on ring gear itself just on the mounting plate (if that's what it's called) of ring gear.Ya water definitely got in there before it sat for a while. How does the actual ring gear look? Any rust on the teeth? The surface rust on the ring side of the case and the inside of the cover can certainly be cleaned off with scotch Brite or brass brush. Rust on the actual gears would be another story.
called the "carrier". as said, somebody got water in the diff and it sat for a while. I wouldn't be worried about what you see - you can clean most of it off with a wire brush. Blow out the dust with air & brake cleaner, let it all dry, clean out the housing well and putting new oil in. I would be worried about the carrier & pinion bearings, which you can't see. If you know how, it might be worth pulling the carrier to inspect the carrier bearing & races.....No rust on ring gear itself just on the mounting plate (if that's what it's called) of ring gear.