In this post I use the typical person’s definition of “alien”, some bug eyed thing with oversized brains and flying saucers, giant spaceships, whatever, and likely with two legs.  There are other and more logical or likely constructs, but we’ll stick to the typical fantasy creation.

We would have the ability to know, but first we would have to look.

The lunar surface is a perfect record of hundreds of millions, if not billions, of years.  The regolith is a “blanket” of pulverized rock a few meters thick.

It’s very simple to deliniate the periods of time and the locations where we could find evidence of aliens, and the periods of time and locations where we could not.

First we’ll limit the discussion to the last billion years.  This gets us past the volcanic period, and past periods of truly intense meteor bombardment.

A.   If a spaceship or an outpost had been built on the Moon a billion of years ago, and by chance a meteor hit in that area, then no trace would be left.  All evidence would be vaporized.

B.  If the visit was so ancient that the evidence was gradually covered in dust, it would not be seen.  Many Earth structures would show their structure through a meter or two of regolith.  Obviously buildings above a certain minimum size would.  Also, remote sensing in IR thermal or radio frequencies would reveal these evidences even though they were “buried.”  There is an estimate of one millimeter per thousand years of regolith dust accumulation, so a hundred million years would be a hundred meters.  We would be unlikely to discover evidence of ET’s visit a hundred million years ago.

C.  If they were extremely careful to leave everything exactly like before they arrived.  This would be very difficult, as it would involve spreading material around to cover up the ground disturbances made not just while moving around on the surface, but also by the spacecraft landing and taking off.

D.  If ET had peeled back the top three centimeters of a surface area, say to mine for He3, then one would think that area would be re blanketed in regolith within fifty or a hundred thousand years.  And that is true, but other marks of the work would likely show a footprint for much longer.  For example, typically in such work the loose surface clutter of debris and various sized rock would be first swept to the side, and would show as a trail of rock, perhaps at certain intervals in parallel.

One interesting type of remote sensing is that done by the Diviner instrument on the LRO spacecraft.  It measures temperature.  It can measure differences in the cooling of areas, say in a lunar eclipse.  A large meteorite resting on the surface would cool down differently than an igneous rock.  A spacecraft or habitat on the surface would show a different heat signature than simple rock.

A simple look at Google or Youtube will find many, many cases of people trying to read things into the Lunar surface that simply aren’t really there.  In many cases what they see is an illusion introduced by camera pixelation.  We are now to the point of having imaged the Moon at 1.5 to 4 meters resolution, the entire surface.  Just as amateur astronomers with their telescopes can discover new things in the sky, it is possible that amateurs examining these massive databases of surface features may find some very interesting things.

So the answer is that if one picks a reasonable time frame – say in the last million years – then it is possible to ask the question if ET may have been on the Moon, and whether we can discover the evidence that he was.   Further, amateurs perusing the LRO datasets could be the ones that found it.

For example, take several dozen artist’s renderings of alien spacecraft, place them on a virtual 3d lunar landscape and cover them with various thicknesses of lunar dirt.