This is a story from the 1950's. I recall that one of the characters states the date of the invasion as 1959. The story has some similarities to Oblivion.
There is a group of people in a penal reservation in the middle of the desert. They believe they are on Mars and their memories have been partially wiped as part of their punishment/rehabilitation. But there are some un-Martian details: the weather is hot and there is only one moon.
These people hunt a species of robotic moles that live among the sand as part of their forced labor. The moles fetch resources from the ground and people fetch the moles.
Eventually, some of the inmates discover that they are not on Mars and flee. I don't remember if they steal a plane or cross a long tunnel in an abandoned mine. It may be both ways.
They discover that Earth has been conquered (in 1959) by metal-skulled aliens with certain similarities to the robotic moles. They have conquered Earth and have erased memories and manipulated a small number of humans to make them exploit Earth's resources.