The only part of the figure you need to worry about staining is the neck and headsculpt.
The best/easiest thing to do is cut a neck guard out of an acid-free card protector and fit it for best protection from the robe. Obviously this won't protect the whole head, but I doubt most people are going to pose this with the hood up.
I'm SURE you can go through the hassle of disassembling, washing, reassembling etc. But with a hidden neck like this figure has, I don't think that hassle is worth the comparative ease of a neck guard.
@Sassafras has accurately described how to do it, should you choose. I will add though, that it takes a few cycles in my experience for the water to run clean. I think my Jedi Luke robe was a 4 or 5 rinse run, in which the first two I used dreft detergent (very delicate) to assist. I think my 4th run was a 25/75 vinegar to water soak/rinse and then I had a final run of clear water. The water in the tupperware was no **** coffee dark for 3 rounds or so. The amount of dye in these is insane.
But, that pic
@McHaleyArt posted is a great comparison. Not only shows the progress in paint HT has had, but what I would call a genuinely successful redesign of a character that reinvents the appearance while staying true to the narrative and original look.
Also the deals on TW are great but 100% indicative of them hemorrhaging money. Digging a hole to fill another one. They've pulled paypal as a payment method, and I just have no interest in taking risks from them after hearing the stories people have experienced.