"Just don't" is often used as a response to the question (or some variation of) "Why not?":
Dad: Don't touch that
Kid: Why not?
Dad: Just don't.
In your example, they're shutting down the question "Why can't I disturb you?", "What are you doing?", etc.. before you have the chance to ask it, implying they are expecting you to ask it.
Dad: Don't touch that
Kid: -
Dad: Just don't.
Of courseIt's quite common, so much so that it has made it's on a Tway into one-Shirt, so is most likelyway conversation for comedic effect, but I thinkhence the point still carriest-shirt print.