Convict them as felons and throw them out. If they return without proper documentation execute them. The rest will learn to follow our laws real quick.
When I was young my father picked apples. The owner of the orchard complained that my dad wasn't picking nearly as many apples as the wetbacks were. My dad asked "did you happen to notice that they are also 'picking' the ones that drop on the ground?"
Ahh, wetbacks. What a lovely story.