Do they throw them away?

I think Qantas does. In fact, Qantas J (and presumably F) class uses those towels in the lavs, instead of paper towels. Passengers then toss them in the trash. Wasteful!

I use them on the hands then wipe the armrests to see how dirty they are. Sometimes they are black! On rare occasions, they are spotless (like when I was in an approximately 7 day old A321 on US.