I wouldn't. And honestly, I doubt she'll even notice. You're over-thinking this.
If you aren't close, and you don't ever speak, she shouldn't be invited. Just because she invited you, doesn't mean you have to invite her. And honestly, she probably invited you for the gift. If she cared at all, you'd have heard from her after the gifts. The fact that you didn't speaks volumes. This woman is not your friend.