Background checks don't provide a full story on everyone entering your home to perform a service, no matter which industry we're speaking of - HVAC, carpet cleaners, remodelers, movers, appliance repairmen, etc. Having your home serviced by anyone requires that you be cautious. Your valuables should be secured prior to the arrival of any serviceman. This includes anything of monetary and/or sentimental value.
In the moving industry, specifically, there are many times when your movers are not in your direct view. You want to be confident that you haven't increased the likelihood that you'll become a victim of theft. Don't label boxes "jewelry" or "electronics." Try using words like "living room" or "closet." Leaving your cell phone or wallet out in plain view is also not recommended.
Stealing is wrong, and we make no excuse for it. We do our best to send you movers who are only interested in providing you with excellent service. If you suspect that your serviceman has stolen something, CALL THE POLICE! Allowing them to leave the location without doing so will only make it harder for you to prove a crime was committed.