'repair' is a bit of a fuzzy concept when you're talking about an archaeological site, though, still more when we're talking about a site that was caught up in a volcanic eruption.

You can literally never repair it to the state it was in before the robbery, in the sense of restoring it to a pristine condition as it was left by the eruption.

You can also literally never step in the same river twice, but that's a bit more metaphysical than literal. Photos by the robbers before they vandalized the site would be invaluable. Nowhere near as good as if they'd left it intact, but better than nothing.

The whole question of this thread is how they are putting a ‘value’ on the damage done.

If photos (which presumably do not exist) of the site in pristine pre-robbery condition existed would be, as you say, ‘invaluable’, then how can we put a value on the damage done?