Haven’t read everyone’s replies, but YANBU in my book.
Your DD is 13, a member of your home life, and you have responsibility for her. Your parents should not be bypassing you.
How do they know whether you’ve set her chores to do over lunch? Or that she was feeling a little under the weather this morning and should be home resting? Or that you’re all going out for a family meal tonight so really she should have a sandwich lunch today? It needn’t be anything sinister.
In fact, making plans directly with a 13yo, when you have an inkling this may not be totally fine with the parents, smacks of deliberately going behind your back.
It’s controlling on your parents’ part, of you. They’re showing you they don’t need your permission to take their granddaughter out to lunch, whatever else may be going on. Their relationship with her overrides yours.
You’re “controlling” your 13yo’s movements because she’s a child and you should (someone needs to at that age, and typically it’s a parent). It’s not really control as you’d have been fine with it anyway and said yes - in this specific instance it’s just going through you as an FYI and checking nothing else going on.
So no. YANBU. I’m surprised at how many people seem to think it’s fine.