I think "claiming" is pretty straight forward. To claim anything, realworld, you pretty much just say "thats mine".
I doubt it is that open. It likely means that you have to do something with the bodies.
Why? The distinction "unless claimed or moved" is already made, so clearly you can claim, rather than move (or vice-versa), and claiming is really nothing more than asserting ownership. Seems to me calling "dibs" would be sufficient for "erfworld", and the corpses wouldn't up-pop.