This house had limited influence in the Klingon Empire in the 2370. It was major enemies of the House of D'gor for seven generations. Rather then honorablally challemge them, they chose to dishonor them by course of systematically undermining them and taking their money and land.
In 2371, Kozak was killed in Quarks. He had no male heirs so he left his house leaderless. If the house fell D'Jor would make a claim for its title as well as properties. He arrived at Deep Space Nine and got Quark to claim that he deafeated Kozak in combat. If he didn't the Klingon High Council might have gave Kozaks house to his wife.