I don't think there's any "should" in this situation -- whatever you guys have agreed on is fine.
If I were you, unless you specifically talk to her about it and change your arrangement, I would probably continue sending snacks. If the cupboards were bare and it wasn't a babysitting day, you'd find something for them to eat or go shopping and get something, right? And since your babysitter isn't used to having to feed them, she could be having a bare-cupboard day that same day, so you can't assume she'll have something on the days you don't.
If I were you, unless you specifically talk to her about it and change your arrangement, I would probably continue sending snacks. If the cupboards were bare and it wasn't a babysitting day, you'd find something for them to eat or go shopping and get something, right? And since your babysitter isn't used to having to feed them, she could be having a bare-cupboard day that same day, so you can't assume she'll have something on the days you don't.












I wouldn't let them eat a whole meal of my food if their parents were sending food with them, but they could certainly have a bit to see if they like it.