Hello.

I've had the problem recently (I'm just starting the learning process), of getting called on my FTC's.

After a minute or so, I'll have someone, either the target or another person in the group, ask me "Didn't you have to go?"

Is their a proper response to this, does it happen often, or does it just mean I need to up game by a few notches.

Either you aren't engaging them enough (which seems the more obvious reason) or, you're probably saying your false time restraint wrong, I usually say it casually, in a "no big deal" sort of way.
I think it's probably because you are not engaging the group as a whole, or you're just boring them.
Although maybe they could just be thinking "oh this guy is going to forget about getting back to his friends" or something along those lines. So by her saying didn't you have to go, it could be that you haven't said the FTC casually enough and they think you forgot about your friends, or they want you to leave because you are boring them. Just read the situation and see which category you fall under, how did she say it? Did the group/target enjoy your presence?

"ohhh you don't want me here? trying to get rid of me?" I don't know how you might be engaging them, but this line could work if you say it well. Try to convey that you don't actually care, but you are saying it in a teasing way as if she actually hurt you, but it's obvious she didn't.