So apparently you have to complete the Side Quest: Blood on the Ice in order to get the house Hjerim in Windhelm cleaned.
The strategy guide says at the end of that quest one of the rewards is "A free "cleaning" of Hjerim, so the gruesome antechamber has the flesh and bones removed from it, whether you own the house or not."
Spoiler In order to start this quest you must enter Windhelm and then leave the hold and travel somewhere else, return again and do this a total of four times. Then when you return the fourth time go to the graveyard in Windhelm and you'll trigger the start of the quest where the gathering of people are.