I would say that she knows exactly why you are avoiding her and because everyone else knows that she will not be included she is treading carefully, ie, I mean where she would normally personally confront you, she has decided to try and clear it up without a personal confrontation. She probably knows you well enough to realise you wouldn't handle it well and the only reason she is being careful is because if she upsets you too much everyone else might find out about it and she looks like "the bad guy"
To me, this is the crux of the issue. Does UnwantedGuest know she's a bully and why people avoid her? I tend to agree with Rusty, but I'm not 100% sure. What do others think?
If UnwantedGuest knows she's a bully and this is another tactic to reel OP back in and play mind games with OP again and again, then OP's best bet is to ignore. Ignore the narcissist. That is the thing that angers them most. And why waste your time and energy giving her the pleasure and reward of knowing that she got to you? If her goal was to be mean and hurt you in the past, you're telling her she succeeded.
However, she could just be a very brash person who is not good at seeing the world through the eyes of others. She certainly wouldn't be friends with someone like herself, but does she have the ability to see herself from a distance? Not that it's OP's responsibility to educate her. And even if OP had the perfect phrase which was entirely true, UnwantedGuest likely still wouldn't get it and take it to heart, learn from it and change.
But I think if we're all pretty certain UnwantedGuest knows what she did wrong, then the answer is to pretend you're a blackhole and ignore. If UnwantedGuest is dense, should anything be said back other than "leave me alone"?
And, fnygirl, if you do reply via text or email, make sure it's something you're ok with UnwantedGuest forwarding and showing to all of your friends and her friends. Because she's going to use it to make herself look like the wounded party.