TSA broke a lock for which they have a master key. How can I claim compensation?

Note (from Yale):

TSA Security Officers inspect more than 2 million pieces of baggage every day. It is faster and easier for them to open your Travel Sentry locks using their special Travel Sentry tools than it is for them to cut or break open a lock. However, it is rare but possible, that the TSA may have to cut open a Travel Sentry lock if it has been damaged or malfunctioning in some way. Should this occur, TSA is not liable for damage to your lock.

My emboldening.

If a TSA source is preferred:

TSA is not liable for damage caused to locked bags that must be opened for security purposes.

And in case of any doubt, you won't receive 'compensation' for this.

The only online mechanism for filing claims is through the claims page on the TSA website.

You may file a claim if you are injured or your property is lost or damaged during the screening process. Screening at certain airports is performed by private companies and not TSA.

However, don't anticipate a speedy resolution:

Please allow up to six months to fully investigate your claim. Claims that require investigation by law enforcement require additional processing time.

You can try your airline, especially if you have status. TSA simply has stolen my hasps (or caused them to become lost by not closing them back) and United has compensated me. Of course that was just $25 for the two hasps so that was not a big deal.

The following is just speculation from me: these hasps force them to use the master keys, even with bolt cutters cutting through a 1/4" steel hasp is not easy. So they opened it and then made sure no other screener needs to do such a thing again. I learned my lesson and use zip ties to close my bags now. The scenario is completely tilted towards cutting: it's faster (master keys can be very fiddly) and they are not held responsible for pretty much anything.

Edit because of comments: this is the hasp and it is for Pelican cases to keep luggage handlers out. They can damage it but getting into the case, nope:

Your case is brand new? If so, it probably has a warranty. Easiest thing would be to contact Antler, say your TSA lock was defective and had to be broken open, and they will send you a new one. It will be a lot less hassle than your insurance company (whose excess will eat up most of your compensation) or dealing with the TSA, the airport, or the airline.

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...

1. 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.
2. 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".