My exBPD did the same after the breakup.
I think she did it to convince both me and herself that she is not evil.
I don't know what the best way of reacting would be. It's a loose/loose situation.
If you write her back "thank you", her ego will be stroked because she will know that she got your attention.
If you ignore the text, her ego will be stroked because she will think you are bitter and angry and that she is the sane person who has the curtsey of being polite to somebody on their birthday.
The best way to respond is delete and not to think how her ego feels. You have given to much of your sanity and kindness already.
Try to focus on yourself for a change
