According to this page on usatoday.com: Lost, stolen, broken: TSA pays millions for bag claims, USA TODAY investigation finds
"TSA officials say the agency accepts claims for damage to locks, and they concede that agents sometimes break locks to inspect bags."
So, I would file a claim with TSA.
The only problem I see is that unless the note that TSA left in your bag indicates that they damaged the bag to gain entry, you don't actually know who damaged your bag. But...
- It's not obvious from the picture but it's probably obvious looking at the bag that the zipper tabs were intentionally cut, rather than somehow being accidentally damaged by interaction with airport equipment.
- There may be surveillance video of the inspection process that might show the bag being damaged by the TSA.
One suggestion from @Joshua that I like is to try to obtain a duplicate master key and demonstrate whether it works, or not. If it works, you have some proof TSA inappropriately damaged your bag. If it doesn't work, (and it does work on other bags), it indicates the lock is defective and you have a good reason to file a warranty claim with the manufacturer of the bag/lock.
Others have said something like: "Why would the TSA agent take the extra effort to damage the bag to gain entry, rather than to use their key?"
It is not unreasonable that the TSA agent: Improperly used their key, used the wrong key, couldn't find their key, couldn't be bothered to waste their time to obtain the correct key, and used their trusty fallback "universal key".