The Thrust Washer will usually come off the Idler Gear, but sometimes needs 'help'. Whether it can be used again or not, you won't know until you do get them apart.
In regards to the Transfer Housing - how does the Gearbox side also look? Looking at the Transfer Case, a little hard to say with certainty, but it looks like the wear is deep in one part than the rest of it. Also, looking at the shaft of the Idler Gear, it seems like it's had more load on the end of it than across the whole of the bearing area of the shaft. If that's the case, then the Housing is mis-aligned to the Gearbox and this will have been the cause of these issues. Dressing it and freeing (or replacing) the Idler Gear and Thrust Washer will only result in the same happening again.
Check the Out-rigger Bearing on the First Motion Shaft Nose too.
If the Housings are misaligned, you could of course try different ones, but there's no guarantee here that they'll be any better - could be worse!
I had one recent that was real bad (0.9 mm misalignment) and chewed out the bearings and thrust faces in 10 000 miles. It also chewed out the Out-rigger Bearing too.
There are Stepped Dowels to coff coff maintain alignment between the Housing and the Gearbox. What I did was to remove these dowels, mount the Gearbox in the Mill, fit some Dummy Shafts to both Idler Gear Bearing and First Motion Shaft Bearing Tunnels, clock up (and log) the location of the Dowel Holes in the Gearbox (they are 7/16" dia on this side), fit the Housing and nip it up on the Studs, then re-bore the Housing on the Centres for the Dowels in the Gearbox (parallel), Turned up some 7/16" Dowels (in Stainless) and fitted those to the Gearbox.
There's no doubt other ways to skin this cat, but that was the best way I could come up with. Carbon mentioned to me that Vizard has a method mentioned in his book 'How to Modify your Mini', which I did read up on but I wasn't crazy about.
It didn't quite end there for this one as the tunnel for the Idler Gear Bearing was distorted too (in both the Housing and Gearbox). The Bearings just fell out.