When Yeung Gor joined Kublai Khan's newly hired retinue of mercenary warriors, their top priority was to kill Gwok Jing and penetrate Seung Yeung Fortress' defenses. Given this, it's a wonder that they got so involved in the affairs of Passionless Valley.
Yeung Gor and the Mongol mercenaries originally went to Passionless Valley to rescue Chow Bak Tung, who had supposedly been "captured" by the people of Passionless Valley. Yeung Gor, naturally, wanted to help his friend, but I don't see why the Mongol mercenaries starting with the Golden Wheel Monk were so eager to join him. *They* were not friends of Chow Bak Tung and in fact, knowing that Chow Bak Tung was one of Gwok Jing's most powerful allies, they would have welcomed the idea that Passionless Valley might eliminate Chow Bak Tung for them. Moreover, Yeung Gor fully realized that with Chow Bak Tung's martial arts might, the people of Passionless Valley really posed no threat to him: he let them capture him because it was another fun "game" he could play. Yeung Gor and the Mongol mercenaries did not have time to waste on this: they urgently needed to kill Gwok Jing (in Yeung Gor's case, for supposed revenge and in the mercenaries' case, to facilitate the Mongol invasion of southern China). As it was, getting involved with Passionless Valley got Yeung Gor into a whole new world of trouble.