Thanks for the responses, which I appreciate!
Someone asked if the books are multiple copies of the same thing or all different. They are all different, each single copies of a distinct book.
I can't imagine the woman who does this event doing something like a lottery or a more time-consuming, formal way of giving out the books. I don't think I can try to impose that sort of structure on her; she's a very informal person (and it would feel like overstepping to me to tell her to run a lottery, limit them to one apiece and give the others to non-attendees, etc..). I would bet that before she'd put that kind of formal structure in place, she'd just stop giving the books to the girls. Also it wouldn't be in this bookstore's character to be giving out free books to people who aren't in the book group. And the leader is not the owner of the store (it's a small regional chain, with a number of stores).
But it is maddening that this one girl scooped up a full half of the bounty, and she really grabbed the best ones. So disheartening to see bad manners rewarded and good manners punished. My own daughter only got one book, which she ended up disliking and won't even finish reading, and there were some delightful looking books in that greedy girl's arms.
I do think I will bring it up to the leader of the book group and say that lately there has been an issue with a single girl grabbing a huge number of the books before the others can even glance at them (the one girl moved like lightning).
Anyway we are lucky to have this woman doing this program. Both my daughters have loved participating in the book group. We've found some great books as a result (and read some books we didn't like, but that's okay, too) and had some nice moments discussing them with other moms & tweens, and the group sends questions to authors, who write back to us. Evidently there are some authors who have formed a sort of sentimental attachment to our book club from afar as a result of that, a couple of whom sent some little token gifts to the girls and one who came to the group to visit it, and only two authors over the last several years declined to answer our questions. So you can see I am operating from a position of gratitude and not wanting to complain overall.