I have to agree with hm – us and penguin about “obtrusive” in its present-day use and can only conclude I was half asleep when I endorsed it in this context last night. Sorry for laying a false trail.
Its sense when applied to people and things nowadays tends in the direction of (zu) auffällig, whereas aufdringlich DWDS defines or glosses as zudringlich, lästig, Duden as sich aufdrängend, lästig fallend, [durch Bitten, Fragen o.Ä.] andere belästigend.
---so “pushy,” “intrusive,” and Hecuba – UK’s “heavy-handed” are the candidates in this context.
Re "invasive." It’s certainly used in the context of invading people's personal space. But I’d reserve it for contexts where what’s really required is, say, übergriffig; aufdringlich, it seems to me, is a good deal less specific, in the OP's context at least.