Fairly certain I read this story on paper, possibly in a science fiction anthology. Probably read it no earlier than 12 years ago, and it was probably either something written in the '90s or later, or something by a Golden Age author like Heinlein, Asimov, or Clarke.
The plot is roughly as follows:
A moon landing mission involves a new astronaut who has not been to the moon before. He is accompanied by a veteran of a previous landing mission. The veteran proceeds to introduce him to a secret known only to astronauts: that there is a small house with a lawn and a white picket fence on the moon. An old couple lives there with a dog. They visit the house, and it is somehow in some sort of bubble of existence with normal Earth properties -- air, gravity, etc. As I recall, this "bubble" is not visible to the naked eye -- it just begins/ends outside the fence.
The couple is always kind to visiting astronauts, and greets them as friends. When the veteran astronaut is momentarily alone with the new astronaut, he quietly mentions that previous astronauts visiting the couple even managed to surreptitiously obtain some of the dog's feces to test them, and they appeared to be normal canine feces. He explains that no one has yet figured out how the house has come to be on the moon, or how the people manage to survive there.
The astronauts visit for a while and then leave. I believe they take pains not to point out the impossibility of the situation, out of politeness. If I recall correctly, it is feared that confrontation with the couple could cause them to leave or disappear, which would prevent scientists from ever figuring out how they got there.
I believe that later, the new astronaut hears that the house has disappeared. It might be because the couple was inadvertently offended by a visitor, or because the husband decided that "the neighborhood was getting too crowded" -- I cannot recall. It is intimated that the house with the couple living in it still exists on the moon, just moved to a different spot, where they await to be rediscovered and visited by lunar explorers in the future.