I have no problem with companies having property on the moon, as long as they realize that they have precisely zero ability to actually enforce any property rights or hold anyone personally accountable for violating any such rights unless there is somebody who is personally there, or at least until they personally return to the earth.
In general, such ownership rights should immediately dissolve when nobody who represents said ownership is living there, only becoming permanent once large enough permanent settlements are built on the moon that a 24/7 law-enforcement infrastructure can be implemented to enforce such property rights.
Until that time, if you mess around with property that belongs to somebody else on the moon when nobody who represents them is there to physically stop you, without authorization from the company that owned it, you would probably encounter a lot of difficulties when you returned to earth, unless you happened to live in a nation that didn't respect the laws of the country that the company belonged to anyways.
The entire notion of property is a consequence of civilization, and if you don't have a civilization living there, then you can't really have any permanent property there either.