You can't stop people from pirating your app. Not to mention, I'm sure most of us have pirated something, at some point, as well. I'd personally let them keep the files up. As it's been said, another user is another user. He'll show it to his friends who might buy it instead of pirating.
Another option to help fight people pirating would be to offer a free version. Maybe limit how many things they can add to their list, and have it ad supported. The full version you pay for and gets unlimited items in their list.
If you do find a way to detect someone using a pirated version, instead of disabling the application, why not do something fun like create a "pirate theme" that gets applied so they know they've been busted. (The only drawback is if the pirate theme is awesome you might get people pirating it just to see what it looks like).
There's no sense in fighting pirating, it's never worked. As far as I know, no industry has had any real success stopping it. I say embrace it and try to use it to your advantage.