Border Patrol Does NOT check if illegal aliens have a criminal records outside US!
The criminal background check conducted by Border Patrol is compared with known criminal record databases in the United States ONLY
and is part of the processing of the illegal immigrants by their
agency. This is done through fingerprint comparison. During the
screening process, Border Patrol also routinely questions illegal
immigrants on gang affiliations in their country of origin. Information
obtained during this process is used to determine whether they remain in
detention or released pending a hearing date.
http://www.murrieta.org/faqs/categoryqna.asp?id=38#572