While the pepper may burn a little, I can't imagine the child is physically harmed. Nor can I imagine the child will carry some emotional burden from this punishment that would require years of therapy. I would say that this is a little strange, but nothing to warrant someone meddling in another's affairs.
False accusations can inflict great damage on someones life.
If the child's mouth was full of open sores from the pepper, you may wish to contact the parent. She may not even realize that she was harming her child, but instead just grasping for some form of punishment, perhaps even one she experienced as a child. Heavy bruising, burns, broken bones, lacerations, etc are far more serious and cases of such child abuse overwhelm the social service offices. I would hope you will really think about what you are accusing this mother of. I think this is child abuse.