My dad used to have one of these cards (printed on Day-Glo orange card stock) in the sweatband of his hat, along with his business card. I never took them to be something to ward off hat thieves, or even people who want to inappropriately handle your hat. Since, back in the day, there were a lot of men wearing the same style of hat, I figured it was for the guy who accidentally picks up a hat that looks like his but isn't. He would quickly notice the error by seeing the card, more quickly than he would be reading the business card and seeing if it was his, particularly since the sweat band obscures a lot of the business card. And even if everybody had "Like Hell it's yours" cards, there was probably enough variation to help quickly tell hats apart.
We have a thread titled “Ask a Question, Get an Answer” where you can post these types of questions. We prefer to not have new threads started when the subject otherwise fits in an existing thread; it gets cumbersome to find things if we don’t do this. Also, be prepared for a bartender (site moderator) to merge your thread(s) into another thread. It’s just what we all go through when we’re new here. No harm done. I hope you stick around and keep posting photos of your hats!