That repetitive, mocking hand puppet whose puppeteer we never see. Some immaturely playful housemate? An ill-advised accomplice for the killer? It couldn't be the killer himself, unless Mengele produced a mutant capable of teleportation.
I think the filmmakers just wanted to throw in something colorful and creepy with little regard for artistry or sense.
...either that , or the makers wanted to hold off on showing the audience the likeness of all these kids for as long as possible , and for us to find out at the same time as Ezra Lieberman. It's also possible that they wanted to show us the unpredictability of these kids...one minute he's just a kid playing with a puppet, the next he's answering the front door like a spoilt little *beep* and being very rude.
I think it's a subtle clue - a way of showing the boy without showing him. The audience learns that a boy lives in the house, but we don't find out that he looks exactly like the first boy. Thus, the big surprise is delayed until we see the third boy.
Also, since the boy is playing with a puppet, this scene hints at two things: (1) the boy has an artistic streak; (2) the boy is kind of weird. I mean, what kind of 13-year-old spends that much time making a puppet cackle into a phone? Altogether, this scene adds to the movie's creepy atmosphere.
Yes, this. Plus the child was using a puppet from Punch & Judy, a show notorious for its violence. I think its use was to demonstrate early emotional detachment of the child and a penchant for cruelty.