The cleaner is very lightweight and brass wool grabs the tip, so everything lifts together when you try to pull soldering iron back. Maybe it only happens with TS80P tips because they are thicker near the end, and with more thin and uniform tips of older types everything may be okay, but nevertheless. Also, rubber feet don't work on my table and anti-static mat.
The thing cleans the soldering tip decently, though. But it can be achieved even without this bulky holder, just with a piece of brass wool. So it's 2/5 overall for this price. I bought it primarily for UX, but it fails to provide it properly for me, sadly.
Hope it will suit somebody's else needs better.