It wouldn't bother me at all if a friend gave away a book I gave her. I mean, in my world, books are meant to circulate. I keep a lot of books, loan them out, and if they come back, good, if not, then no big deal. (Well, for most of them. If I do care, I say "I need this one back", and my friends happily comply.)
To me, if someone gave a book I gave them to someone else, I'd be flattered, because that meant they thought it was good, or at least, that the other person would like it.