It doesn't say you have to use TSA locks, it says the gun case has to be secured (locked) by key or combination. I used a Master padlock, the hard-sided case was opened and examined by ticket folks to insure the firearms were unloaded and no ammo was in the case and again by the TSA agent. Each time I gave them the key which was returned to me after they finished their inspection. At no time during this process was the case or firearms out of my vision.
Following is a summary of key regulatory requirements to transport firearms, firearm parts or ammunition in checked baggage:
All firearms must be declared to the air carrier during the ticket counter check-in process.
The firearm must be unloaded.
The firearm must be carried in a hard-sided container.
The container must be locked.
The passenger must provide the key or combination to the screener if it is necessary to open the container, and then remain present during screening to take back possession of the key after the container is cleared.
Any ammunition transported must be securely packed in fiber (such as cardboard), wood or metal boxes or other packaging specifically designed to carry small amounts of ammunition.
Firearm magazines/clips do not satisfy the packaging requirement unless they provide a complete and secure enclosure of the ammunition (e.g., by securely covering the exposed portions of the magazine or by securely placing the magazine in a pouch, holder, holster or lanyard).
The ammunition may also be located in the same hard-sided case as the firearm, as long as it is properly packed as described above.
Black powder and percussion caps used with black-powder type firearms are not permitted in carry-on or checked baggage.