Yes. After the Church mission and the Good Ending. Not sure if you can otherwise. However Trashed will probably not go up to 'New'. I think they only go up by 2 stages. So like 'Heavily Used' becomes 'Near Mint' while 'Used' and 'Near Mint' become 'New'. If I understand it correctly anyways. I've only really used it on Used and Near Mint. But Shanice does say she can't turn trash into treasure.