You can see that alongside the tumblers there is also a small keyhole. That accepts TSA keys. Assuming the lock itself is not broken, the TSA should have no trouble opening it. That's what being a TSA-approved lock means. So within the US, you should have nothing to worry about.
If they have to break in, then yes it's likely that would destroy the lock (or the suitcase itself, depending how they go about it). But the chances of that should be pretty low - chances are your luggage won't be inspected anyway, and even if it is, the TSA master key will open it without any damage unless the lock itself has developed some problem.
In Europe the TSA-approved standard doesn't have any official standing, so they may not have the TSA master keys. If they feel it necessary to inspect the contents of your suitcase, then it's certainly possible that it would be damaged. As Willeke says, this may be covered by travel insurance (check policy details).
That danger of damage may be a reason to avoid relying a TSA lock that can't be circumvented in some other way for travels in Europe. That said, there's nothing especially unusual about similar cases, and while I have seen reports online I've never heard of this happening to anybody I know.