They're not saying "come home" in a literal since, it's their way of voicing that Laika is missed.

Reading about her, she was a great dog. Really kind, never provoked other dogs, and fairly noisy. One Russian scientist involved with Laika's launch said that the loss of Laika wasn't worth the mission, since not much data was gained from it (it was planned to be a days-long mission at least but Laika died from overheating within a few hours from launch due to a failed cooling system).