Using TSA locks is illegal for securing firearm cases. It shall be a lock only you have a key to. Everybody has keys to TSA locks.

The relevant code for transporting firearms as checked baggage 14 CFR 1540.111(c):

In checked baggage. A passenger may not transport or offer for transport in checked baggage or in baggage carried in an inaccessible cargo hold under § 1562.23 of this chapter:

(1) Any loaded firearm(s).

(2) Any unloaded firearm(s) unless—

(i) The passenger declares to the aircraft operator, either orally or in writing, before checking the baggage, that the passenger has a firearm in his or her bag and that it is unloaded;

(ii) The firearm is unloaded;

(iii) The firearm is carried in a hard-sided container; and

(iv) The container in which it is carried is locked, and only the passenger retains the key or combination.

Also, no marking the outside of the luggage with anything that hints that there's a firearm inside:

18 USC 922 (e) "No common or contract carrier shall require or cause any label, tag, or other written notice to be placed on the outside of any package, luggage, or other container that such package, luggage, or other container contains a firearm."