Cat possibly swallowed plastic

I haven't been here in a while but I needed some input. My grandmother keeps putting boxes in my room (future holiday presents) and all of them have tape on them. I live in the basement so that is why she chooses to put the boxes in my room. There is one box in particular they have been chewing on. They have nearly stripped all the tape off one side.

Just now I heard Tyran munching on something. I turn and she's chewing on a piece of plastic or tape. I get up to stop her but then she stops chewing. Note that she does not spit anything out. I grab her really quick and open her mouth. NO plastic found! So I'm not sure if she swallowed it or not but there is a good chance.

Should a vet visit be scheduled or will she pass it fine on her own?

If it wasn't a big piece of tape, I would just watch her carefully and monitor intakes and outputs. If they change, call the vet. If it was a larger piece, then I would call the vet first thing and ask for advice. I've got a plastic eater in my house now too--he goes after plastic bags. I'm constantly having to be alert and consistent about putting away any incoming bags or he'll find them for me. Since there are likely to be other packages, you might see if a spray, like bitter apple, would deter the kitties to prevent future incidents.