They find their way back even if they have been moved in complete darkness by using, indeed, magnetoreception. They can sense the direction of where they come from using the earth magnetic field. I believe there is still some debate about how magnetic fields are sensed by pigeons, the latest fashionable idea being that this is through a "warm" quantum process. I don't know if that's correct, but there is clear evidence that there are magnetic-sensitive cells in the pigeons nervous system (Wu & Dickman, 2007). This will only lead pigeons to the approximate location of their home, but once they are close enough they can recognize where they live visually. Pigeons are released everyday so they know the local environment of their home.
I'm quite sure this has nothing to do with the pigeons mates. This is probably some ridiculous idea people had in the middle-age and people kept repeating it because that sort of intuitively makes sense, but when you think carefully about it, it really doesn't.
Wu, L. Q., & Dickman, J. D. (2012). Neural correlates of a magnetic sense. science, 336(6084), 1054-1057.