The people in the short story “If I Forget Thee, O Earth” are unable to return to the Earth because it has been devastated by a nuclear war. This is stated rather clearly in the story. This concern about nuclear warfare is a staple of fiction from the Cold War era.
This story was written in 1951, six years after the US used atomic bombs against Japan and a year before hydrogen bombs were first tested. This was the beginning of the Cold War. The Korean War was in full swing and there were serious worries about the potential for nuclear war.
In this climate, it is not surprising that authors like Arthur C. Clarke would write stories in which the Earth was destroyed or badly damaged by nuclear warfare. We can clearly see that this is what Clarke meant in this story. When Marvin first sees the Earth, he thinks how beautiful it is and he wonders why they cannot go and live there as it is their “rightful heritage” to do. At that point, Clarke tells us why they cannot return. The narrator says that Marvin
saw that the portion of the disk that should have been in darkness was gleaming faintly with an evil phosphorescence: and he remembered. He was looking upon the funeral pyre of a world—upon the radioactive aftermath of Armageddon. Across a quarter of a million miles of space, the glow of dying atoms was still visible, a perennial reminder of the ruinous past. It would be centuries yet before that deadly glow died from the rocks and life could return again to fill that silent, empty world.
Thus, we can quite clearly see that Clarke is saying that the people cannot return to Earth because it has been destroyed (more precisely, rendered uninhabitable) by nuclear war.