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.