I would definitely want to know if my DD were giving away her underwear, thong or not.
And to what has developed as a secondary issue on this thread, I personally don't see the big deal about a girl, even a young one, wearing a thong. There was a time when I would have said "No way" to my DD wearing one, but the more I think about it...I mean really, what difference does it make? Don't we buy nice panties and lacy bras, etc? And I doubt that it is just so that we can look nice for our SO's...it's because such things make us feel pretty as well. If our DDs get that same feeling from wearing thongs, so what? Assuming of course, that they are keeping them on and not giving them away.
Now, if DS comes home and wants to wear a thong...then we'll have issues, I'm sure!