I am not exactly sure how one would go about performing a background check on students as a private citizen or independent group (not government or law enforcement etal). Students who would potentially misuse the art would be discovered fairly quickly by an observant instructor.
There are companies that'll do that for you - criminal convictions are a matter of public record. Many employers use them to make sure prospective employees don't have a history of theft, for example.
ETA: I'm not talking about the process for getting a Secret clearance, where they interview your neighbors and look into your family and financial history and stuff. I don't think you can get a company to do that for you, though they can sponsor you for the government to do it.