I have a squirrel on my hands...
So, confession time... my kiddo doesn't do this (yet) but um, I did when I was a kid?
I remember doing this as late as age 4 and 5. I had little "places" around the house and I would hide little things. Just as you describe- just kinda whatever. Papers, playing cards, legos, old keys.
I grew out of it. I don't even know if my parents knew. But I also wasn't hiding things people used regularly, like their working car keys, so it was probably not as big an issue.
I enjoyed having a little secret, and the kind of private world that having little objects around the house in "secret" locations afforded me. Not sure if your kiddo is up front about her "squirreling away" or if she is also doing it as part of a sort of private fantasy world kind of play.
As I said, no one did anything about it and I did grow out of it. I remember my mother sometimes cleaning and finding things and she would say "what is this doing here?!" or something but it never stopped me. I just found other places.
I don't know if this would work, but if it is kind of a taking pleasure in hiding/secret kind of thing, have you thought about making your DD a special magic trunk or box? She could keep special things in it like paperclips, paper, some bright post-its, an old key, things like that, and she could hide those around in her special spots? If they are lost, maybe you could say, oh, are those in their super secret magic spot? Or something like that? I have no idea if that would work, just brainstorming. I think I might've responded well to that but who's to say, it's all hindsight at this point. :)
Also, how old is your DD? Because when I was really little I saw an animated version of The Lion The Witch and the Wardrobe and I FULLY believed that if I opened the right cabinet or looked behind the couch at the right time I could find Narnia. I actually remember leaving a paper cup in my grandma's pantry thinking I would come back and it would be gone and I would KNOW it was an entryway to another place.