I had some fun with a couple of those things when I disassembled a dead TV DVD player. (that filty piece of trash)
When they got dirty I did wash them with water and even used normal solid soap and they did not change shape nor dissolve, they got back to being sticky as when I took them away from the dead piece of trash.
Now, the only thing I didn't test (how could I?) is if they were still thermally conductive as before, so I cannot really say washing them won't damage them.
At least you know that other devices around you contain them as well, so you can... uhm... "borrow" them, or scavenge them if worse comes to worse.