What type of wild mice are you catching? The house mouse (Mus musculus) is the exact same species as the domesticated fancy/feeder mice. I have heard of wild house mice being attracted to fancy/feeders and even a couple cases where wild mice have impregnated the domesticated. They are usually smaller and slip through pretty much any type of bar cage, which is why it's recomended to have them in aquariums and/or bins.

Also it doesnt matter what type of food it is the come where there is food.