killing dwarves is the most efficient but not only way to complete this. if you continue to hunt in tov you will gain proper faction with the quest mob in question and his neighbors, they are on the kromzek faction. however the other giants, the blue ones by the enterances, are on kromrif faction. killing dwarves raises both these factions, killing in tov only raises zek.
so if you kill in tov but avoid killing dwarves you just need to get coh, or sneak past the blue kromrif ones to get to the red guys kromzek in quest area. not easy but you can save drawf faction and get item this way