e.g. Why do you have to write down your car's plate number, by law, if you pay cash for a hotel room? So the law can find you when you're on the run and therefore not using a credit card, of course. This is law enforcement 101, one of the oldest tricks in the book.
It's not just ICE, there must be literally dozens of three letter agencies privy to the same information from Motel 6 and its competitors.