In my experience, people who go on about any subject like this usually are insecure/unhappy with the decisions they've made.
My children go to an independent school. Friends who could not afford the option either don't mention it, and a couple have mentioned they wish they could afford their child to go to an independent school.
The only negative comments we've had are from people who could afford to send their children privately but have chosen not to.
I usually respond along the lines of "We all cut our clothes differently, and it's a free country, so we can spend our money on what we want".
Another friend has a child who is very young in the school year and my child is one of the oldest. Every year, when it's his birthday, she is "shocked" that my child has turned x +1 when her child has only turned x.
It is mildly irritating, but I know her child has struggled academically, and I am sure there is an element of her reassuring herself .
As others have said, don't explain or justify your decisions, but you also don't need to go NC. I probably wouldn't do the whole invite her over and sit her down. I would probably drop a friendly "WhatsApp" and say you and your son found her comments about private schools and his school upsetting (I would give some examples), and you would be grateful if she could refrain from mentioning them around you.
It's difficult to say don't talk about schooling at all because it's a fairly standard conversation for relatives to ask children "how is school etc". If she makes snide marks, I wouldn't want her to then start making a big issue every time anything school-related is mentioned and going, "@Maria1979 is that ok can we ask that?"