Reteaching how checkmate works

I've played chess a few times with family members and I have seen that most of them think that checkmate occurs once you actually capture the king. For instance, in a scholar's mate they would take my queen with their king and let me capture their king with the bishop, THEN they believe the game is over.

How can I break this habit with them and make it clear that the kings are never captured?

In a gentlemen's war the noble's are not harmed. I would pull out the rules you got with your chess board or bring them up online and get them to read what checkmate is....

Don't hurt the King, but do what you want to his wife! Very gentlemanly!

check mate comes from shah mat which means the king is dead.. so I guess you do kill the king.

honestly it doesn't matter tho, just let them get used to it.

Concluding the game when one of the kings gets taken is actually the Death Match or blitz variant of chess. No checks/checkmate. I personally prefer it over normal chess.

The rule of check is only implemented so that patzers don't accidentally lose their king. And checkmate is really just resignation one move before the king gets taken.

Yesterday a boy came to my house. When he  noticed that the chess board was set incorrectly he began insulting me, hounding me for several minutes. Still... he somehow lost the game we played. It's almost as if it doesn't actually matter if the board is upside down or not. Strange.

As I understand, you actually can take the king, but normally the game is just declared over. If they want to waste time taking the king, fine. It's just not necessary since the true end of every game is the ability to take the king.

Well, there's also stalemate. I guess that also doesn't exist in Death Match chess? Would change a lot of endgame theory... What about castling over an attacked square?

The version I play does include stalemate, but I'm certain that this can be played without stalemate.

When castling over an attacked square, the attacking piece may capture the king. (Even if the king ends up outside of the attacker's range - similar to en-passant).