This quest appears if you have imported a save from Dragon Age: Origins that has completed the quest The Urn of Sacred Ashes without defiling the ashes, didn't send Brother Genitivi home to Denerim, and allowed him to return with an expedition, or you chose "The Martyr" import from the pre-made selections at the start of the game.
When you first enter Lowtown, standing near the Weaponsmithy is a con man surrounded by a crowd, claiming to sell the Sacred Ashes of Andraste retrieved from Mount Daverus. After "curing" a member of the crowd, the crowd will be broken up by Sergeant Melindra of the Kirkwall City Guard. This event happens outside of dialogue, and standing nearby and watching it isn't required to begin the quest. Talking to Sergeant Melindra afterward gives you the quest. There is extra dialogue if Aveline is in the party.
Eliminate the Carta swindlers operating in Lowtown. They are located in the northern part of Lowtown, near Gamlen's House. Return to Sergeant Melindra in Lowtown during the day for the reward.