I was fired from Dunkin Donuts?

for giving away a free coffee to my sister. I worked at a Shaw's DD alone, and right when I gave her the coffee and she walked away, my boss caught me. Bad timing I know. The only thing that made me angry about getting fired, is that EVERYBODY does it...you'll know what I am talking about if you work at DD. ANYWAY, I moved..( I was fired 5 months ago by the way) ..and I was going to try to apply to the one in this town. If I don't add DD to my previous employment, and deny working there before..can they somehow find out and catch me? Or should I just take my chances and be honest and say I've learned my lesson and I wont screw up again. HELP!;)