I think people are being very hard on the parents.
They could, maybe should, have said something, but I could easily see being so flummoxed by the situation that nothing seemed right ... and hence saying nothing at all (and regretting it later).
Also, I wonder if both parents saw this. If the parent who is not related to the family witnessed it and the other didn't, I could see shying away from the inevitable conflict to be considered the lesser of two evils. (For example, I would not want to get into it with my SIL.) It's not my place to tell her she's being rude, even if I think she is.
I can actually see the parents wondering what the heck they should be doing now on their own. I don't think it'd occur to me, after the fact, that I could/should give the bracelets back to the original giver. The sister did have the right to dispose of them as she saw fit. It was the way she did it that was rude (and fairly silly, considering).
Edited to add that I don't see anywhere in the OP that the kids asked for the bracelets. If they did, that's different. I'd be telling my boys, "Oh, no, you don't do that." If the sister just said, "Hey, you can have these!" that's when the above comes into play.