I agree with Angie. Mom may or may not even know the child brought home the little wuggle thing. And if she did happen to see it or notice that it was new, her daughter may have lied about it. (So & So gave it to me, the teacher gave it as a prize, etc). So Mom may be clueless. I will also say, that often, kids that age DO swap toys or things with each other without letting their parents know and without the permission of their parents. While that is not what happened in this case, be aware that you may run into that in the future, and this would be a great time to talk to your kiddo about the "rules" of exchanging items or giving/receiving gifts from friends.
I'd call the mom and give her a "heads up" and do it without accusing but just informing her because you know how hard this stuff is for kids to navigate, and you want her to do the same for you, and blah blah .... Tell her about how kids will give things away without asking their parents, too, and it is not always ok. There are all sorts of things kids have to figure out... and they need guidance.
I probably would NOT share with the other mom that I had contacted the other parent though. Hopefully, you will find out from her that "you won't believe it.... Susie came home today and said that Janie brought her wuggle pet back and apologized!" But, if that doesn't happen, YOU don't want to be in the middle. :/