When the couple returned to Earth, the first thing they did was check on Saly, who was, once again, forced to go to school to learn basic knowledge and properly grow up. Arthur didn't see why Lucy insisted about sending their daughter to school but he didn't object and remained silent. Perhaps she sees the earthly knowledge as something useful Saly could use when she grows up.
Once they were done with that matter, they headed to the gloomy and cold cave where Claudia's bastard son and the doctor were.
It has only been a short while since they were kidnapped but it became apparent how mentally tired and hungry they were, especially the young man, who wasn't as patient and tolerant as the old man.
In the time they were left alone, they conversed about many things but still couldn't find a relation between the two of them except that the doctor knows of the youth's mother, though they weren't particularly close.