According to Science, by the end of this month NASA is expected to come up with a set of “recommendations” for spacecraft and astronauts visiting the “U.S. government property on the moon.” Of course, these recommendations will not be legally binding as the 1967 Outer Space Treaty makes it clear that the lunar surface has no owner.
Despite the lack of ownership, NASA is hopeful that other countries will respect the U.S. sentiments. Incidentally, the restriction list contains more than the historical sites. For instance, the list includes studying discarded food and abandoned astronaut faeces.