The concept of wrecks and salvage also covers protection of sites. But I was just answering the direct question of "who do these items belong to" Salvage law is clear - they continue to belong to the original owner, but IF they are recovered, and the owner wants them back, then payment of some sort must be made.

of course, right now there is no clearly-defined law in space, but my assumption that general international marine law should apply is a reasonable one, since marine law was originally developed to cover the "high seas" which are beyons any single nation's jurisdiction. You can't get much of a higher sea than the big black one up there...

Like yourself, I'd love to see a future Lunar Museaum with a glass dome over the original landing sites. And I'd LOVE it to be in my lifetime and for me to visit! 8-)