Why do you care? It's only a competition if you are part of it. You are making one, if you ignore her, she will just be
Why do you tell her your child's level? Just ignore, tell her you don't know, that you don't care. It's none of her business.
I don't blame other parents to have a look at other children's work, that's quite natural. Parents wants to know where their own children stand. You have a good idea of the average level expected when you have several kids, but when you only have one, it's harder. It it's used to mock or gloat, it's rude, but if it's too understand where your own child is, why not.
Rummaging through school bag is more than rude, I would have been furious.
With competitive parents, if you really cannot avoid them, just play down your own kids, it's quite amusing and it stops the conversation. Other parents who are not your friends are of no importance whatsoever in your life.