Thank you for writing. Since your husband knows her and you don’t, perhaps you should trust his instincts on this. It does occur to me that if you and your husband sometimes do respond (and sometimes don’t), she isn’t getting a consistent message. It may be better to either not respond at all or, if your husband feels he has to say something, to keep it short and neutral like, “Have a nice day”. Whichever — it’s important to do the same thing every time.
Apparently, his ex can’t quite let him go. But since she attempts contact only every 6 months to a year, it may be prudent just to ignore her. Though unwelcome, from what you told me, her contacts aren’t dangerous. She can only upset you if you let her. Maybe it’s possible to just sigh and say to yourself “There she goes again…” and move on with your day.
I wish you ell.