I have never heard that, so if the person you asked has a reference it would be appreciated.
To the OP: Officially, there is not a lot that can be done:
a) There is no provision in Canon Law that I am aware of that would allow anyone to remove the Pope for any reason. The Pope remains Pope until he dies or voluntarily resigns. Period.
b) The College Of Cardinals only officially meets for two reasons: (1) the Pope is dead or has resigned and a new one needs to be elected or (2) The Pope calls them into session to advise him on some issue. They cannot officially meet on their own for any other purpose as far as I can see.
c) The wishes of the Pope need to be followed regardless of his mental state (Canon Law seems clear: “No appeal or recourse is permitted against a sentence or decree of the Roman Pontiff.” - Canon 333.3)
So what can you say to your CCD class? I have tackled the same question in mine and here is my response:
“As Vicar of Christ, the Pope exercises full and complete authority and cannot be removed for any reason. If he were to lose the ability to make rational decisions (e.g. if the Pope said all of the faithful must only root for the Dallas Cowboys) he would still be Pope and his wishes would still need to be followed by the faithful. In this case, those close to the Pope would try their best to either get him to resign or ensure he truly understands what he is asking. In any event, even if the Pope were senile, the Holy Spirit would still prevent him from teaching wrongly in matters of faith or morals.”