Right, if you put your tip on your card (or the restaurant adds it automatically), that's going to have a record because it's not in cash. The restaurant owners want this because having the records of tips means they don't have to pay more than the tipped minimum wage if your tips + the base rate >= standard minimum wage. They want to be able to prove to the government you got your full minimum wage, so they want you to use a card for tipping.
Your server probably still prefers you to leave the line blank and tip in cash though.
That theoretically makes sense, but I've never actually seen that. If I'm paying with card, it's almost always added to the total bill, so there's always a record.