The answer to this question can be found in the second paragraph of “The Interlopers.” The feud between the Gradwitz and the Znaeym families started when there was a lawsuit between the two families in the time of the grandfathers of the two men who will figure prominently in this story.
The beginning of the story tells us that the Gradwitz family has a large amount of land that is very good for hunting. However, on the night that the story takes place, Ulrich von Gradwitz is out patrolling a bit of land on the very edge of his property. This piece of land is not really all that valuable for hunting, but he still values it above any other because of its role in this feud.
The narrator tells us that
A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners…
This family was the Znaeym family. After the law suit, they did not accept the judgement and continued to believe that the land was theirs. Over the years, there were many “poaching affrays and similar scandals” that had made the families hate one another even more. This shows us that the feud in this story started out because of a law suit that had occurred in the time of Ulrich von Gradwitz’s grandfather.