In order to increase your score, you'd have to hunt around in the game and look for these urns to topple over. Problem Sleuth didn't really get to topple any though as none of the urns were ever found.
In Homestuck, a Sacred Urn containing the ashes of Nanna Egbert sits on the mantle of the fireplace in John Egbert's living room. John successfully topples the urn over and spills some onto the floor. He tries to Captchalogue the ash back into the urn, but he
Later, the urn is knocked down again by the impact of a Colonel Sassacre's Daunting Text of Magical Frivolity and Practical Japery book, spilling the ash and accidentally completing John's sprite's tier two prototyping, creating Nannasprite.
In Problem Sleuth, the Ace Dick), "Mystic Ruins Desecrated," (for Problem Sleuth) and "Hallowed Tombs Defiled" (for Pickle Inspector). These parallel the actions of John, Jade, and Rose in Homestuck, respectively.for the characters to score were increasing the number of "Sacred Urns Toppled" (for