"All the cool kids are sleeping with stuffed animals these days"—Fitz, in Book 5: Lodestar
Mrs. Stinkbottom is a bright green gulon stuffed animal. In Neverseen, it was given to Keefe by Elwin, under Sophie's suggestion, when a particular memory about Lady Gisela, previously washed, resurfaces. This revelation threatens to break him from guilt. The guilt manifests as recklessness, leading to a ill-conceived plan to sneak away and storm Ravagog by himself, with nothing more than Mrs. Stinkbottom.
In Lodestar, Keefe leaves Mrs. Stinkbottom behind when he runs away. However, Sophie realizes that it is not in his room. Later in the same book, she finds it in Lord Cassius's room, having leapt there with the starstone found in Cyrah Endal's stall by Caprise Redek. It is assumed that he had been sleeping with it as a way of coping.