The son of Gardar and Arneis is actually alive and will return to seek Vengeance upon Ormar, Snake and all the other in the Ketil Household.
It was basically the last failed attempt by anyone to stop the expansion of his power. Norway and Sweden had to pull an Enemy Mine just to challenge him, and it failed. After that he was the supreme king of "England, Denmark, Norway and some of the Swedes" as he himself put it.
It's right there in the title, after all.
Many chapters post-timeskip, pretty much confirmed that they will at least try to go there.
Killed by Skraeling arrows.
The party is headed for Iceland already. But, then Einar will also reunite with his own family. Then he will make an oath with Bishop Arnald in exchange for help with the expedition to Vinland. And then Arnald will call in the favor before the party is able to set sail again...
This would also fit in with the manga's theme of violence vs. non-violence. Einar hasn't achieved the same level of enlightenment as Thorfinn, so he would be willing to kill for an oath.
It would be interesting to have the party travel so far from the Norse lands only to meet up with the norse yet again in Byzantium.
Why else would there be two Thorfinns? While main Thorfinn is the leader of the Vinland expedition, Bug-eyes will beget a son with Gudrid, the first Norse child to be born in America. Main Thorfinn will hook up with Hild instead.