I've checked my handgun on several flights and always used a *non*-TSA padlock on the gun case. In fact, I thought that's how it was supposed to be.
Never heard of it being proper for TSA to be able to open your gun case themselves. If they need to see it or something, they'd call you on the airport PA. Whenever possible I waited near the TSA X-ray machine until I saw my bag head out the other side and into the baggage system proper.