This reminded me of an incident a few years ago. As a bit of background, When my wife decided to open her packing and shipping business, I decided it was a good time to move my business into a retail location and we shared (and still do share) the retail space.
Well, we setup a rack for business cards right next to the front door. My wife's business also does printing services, so when customers have business cards made up, we offer to let them put some on display in the shop.
About 6 months after opening the retail location, we had someone come in to ship a package. On their way out, this person stopped at the card rack. He removed my business cards and put his computer repair business cards there. Apparently, this Pizza Tech didn't look around and read the sign on the door with my business name nor the fact that 2/3 of the retail space was dedicated to computer peripherals nor the fact that I was standing at the other counter wearing my logoed shirt. I also had a customer at the counter dropping off a computer who noticed what this person was doing.
Needless to say, as far as I can tell, that person lasted in business less than 6 months. It was someone that I never heard of before and when I was doing a periodic review of local competition, he never showed up again.
What I'm getting at is that I believe in Karma in business. Treat your competitors with respect and never talk bad about them and your customers will notice that extra level of professionalism. So, just leave those cards there and, if allowed, put yours next to them. I'm sure someone will notice that your cards are disappearing faster (or might see your competitor playing dirty) and will assume you do better work.