Would an erroneous claim of mate be considered as annoying the opponent, cheating, an illegal move, or something else? Especially in kiddie games, mates are often missed or supposed mates are not really mates. What would the TD declare such misguided claims of mate? What should a TD do if adults did the same thing?
First, kids and adults, the rules are the same, so there is no difference there.

What you are asking about goes beyond just the rules: It comes down to intent.

Whether an adult, or kid, there could be an erroneous claim; and if it is really just that, then the TD should just fix it assuming it is caught in time. It is just a mistake. Other types of mistakes would be similar.

This might be hard to prove, but it an opponent did it just to cheat or annoy, then yes, that would be a breach of the rules, and should be penalized. The real question is how do you prove that? Short of the person having done it before, or bragging about it, I cannot see how a TD would impose sanctions upon someone for what otherwise looks like a human mistake. I think the TD has to assume it is a mistake unless otherwise proven, which again, may be next to impossible. Even without that proof, if the TD suspects, a warning may be in order that future incorrect claims may be sanctioned.