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It is worthless as an artifact and almost certainly worthless as a sentimental object. A kid writing their name in a book is hardly a sign of any particular pride and is really very common (I certainly when through a bookplate phase and none of those books were important to me).
This isn't to say you shouldn't try, there are pretty much three outcomes I see in increasing likelihood (assuming you find her in the first place):
1. It was an important book to her and she's extremely happy to have it back. You're mildly disappointed it wasn't a cooler outcome.
2. It is a meaningless book to her but she gets a kick out of you tracking her down to return it. You both get a laugh out of it.
3. It is a meaningless book to her and she is a bit skeeved out by a stranger showing up with a book she doesn't even remember owning. You're a bit saddened to have caused her even a little distress.
4. It is a meaningless book to her, she says "uh, ok, thanks" and you're disappointed it wasn't something cooler.
So long as you can handle the disappointments for the small chance of something cool then I say go for it. You have a small chance of becoming a story on This American Life and a small chance of worrying she might file a restraining order. But the fun in life is generally in small chances.
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