I'm sure your neighbors are embarrassed but if it is a new puppy, it'll cry for a few days. That's just part of the deal. They must not want it to be an inside dog or they would have it inside with them.

I would say just be an understanding neighbor for a few days. If the dog is still crying after a week, then maybe you can say something. It's obviously an inconvenience for you at the moment but it won't be forever.