After you first give it to Gregory, it can be retrieved from where he hid it in the Storeroom. From here, it is part of the puzzle to steal Angel/Devil Dog's soul. It must be taken from the Storeroom and given to Gregory shortly before he enters the Lounge at 6:30 PM, where Angel Dog is waiting for him. Doing so will cause Gregory to run off to rehide it (in the same place...), causing him to forget about cleaning the Lounge.