"Existing searchable databases from astronomy, biology, earth and planetary sciences all offer low-cost opportunities to seek a footprint of extraterrestrial technology," Davies and Wagner wrote in Searching for Alien Artifacts on the Moon.
"Although there is only a tiny probability that alien technology would have left traces on the moon in the form of an artifact or surface modification of lunar features, this location has the virtue of being close, and of preserving traces for an immense duration.
Systematic scrutiny of the LRO photographic images is being routinely conducted anyway for planetary science purposes, and this program could readily be expanded and outsourced at little extra cost to accommodate SETI goals, after the fashion of the SETI@home and Galaxy Zoo projects." – P.C.W. Davies, R.V. Wagner, Acta Astronautica.
Searching the moon rather than other planetary bodies does is a little random, the two scientists admit.
The Search for Extraterrestrial Intelligences hiding in our photo album
A lot of the reason behind the suggestion aliens might have landed on our moon has more to do with the number of good photos we have of the moon, rather than the greater likelihood that aliens would have landed there rather than elsewhere.
Davies and Wagner don't say the idea of searching existing photos of the moon for aliens is a lot like the guy whose wife found him crawling around the hall and asked him what he was doing.
"I lost a cufflink and I'm looking for it," he told her.
"Where did you lose it?"
"In the living room."
"Why are you looking for it in the hall?"
"Because the light is better out here."
The light, or at least the photos, of the moon are unquestionably better than those of anywhere else in the Solar System.
The moon is also close enough that even amateur astronomers would have a chance to spot alien artifacts with home telescopes as well as LRO photos.