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" pre-built history 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.
Eliminate the Carta swindlers operating in Lowtown. They are located in the northern part of Lowtown, near Gamlen's House. Speaking to them once results in a thinly-veiled warning about "no refunds on the Ashes." Speaking to them a second time begins the fight. Most of them are melee Carta Thugs Critter and Normal-ranked, with the exception of the Swindler, who is an Assassin. If this quest is taken on early in the game the player may not have the abilities or tactics to deal with him effectively. The best place to fight assassins is in tight spaces where players can put their backs to a wall, so retreat out of this open space, past the Hanged Man if need be, which should cause many to break off their pursuit (possibly the Swinder himself) and provide some breathing room from the inevitable reinforcements. Use the full strength of the party against the Swindler, using whatever stun- and interruption-inducing abilities you have, before he's had a chance to deliver too many backstabs, and the remaining Carta Thugs shouldn't be any more difficult than the average group of enemies, as they lack archers. Also, all Carta Thugs in the game are vulnerable to all five elements but especially weak to cold damage, suffering twice as much damage on every point of it, so an Elemental mage with Cone of Cold has the best coverage and damage options.
Return to Sergeant Melindra after the swindlers are dealt with for a reward. If Aveline is in the party, she will make the comment to her that the thieves are dealt with.