How do you respond to passive-aggressive notes around the office? Do the opposite of what they ask for, naturally. Next time, instead of trying to imply something passive-aggressively, just say what you want to say, or better yet – keep your mug at your desk! That’s the only way to assure no one’s going to use it.
Putting up this sign was really asking for it, because we all know that when people are forbidden from touching something, it only makes them want to touch it badly – like museum exhibits. That’s just the way it is, and there’s no point trying to stop it.