Sheldon explains to the FBI agent that Howard once crashed the Mars Rover while trying to impress a woman. This is a reference to the episode The Lizard-Spock Expansion, in which Howard tries to impress Dr. Stephanie Barnett.
FBI Special Agents do not conduct background investigations for security clearances issued by the United States government. All background investigations for security clearances are conducted by Special Investigators for the Office of Personnel Management (OPM). Once OPM completes the investigation, the Special Investigator forwards his or her findings the agency requesting the investigation (the Department of Defense, in this case), and that agency makes a determination based on OPM's investigation whether or not to issue the security clearance. Since Howard is not applying for a job with the FBI, the FBI would not be involved in determining whether or not he received a security clearance.