"The Cad and the Hat" is the fifteenth episode of Season 28.
When Bart betrays Lisa, he has to deal with his guilt – literally. Meanwhile, Springfield is surprised when Homer is revealed to be a chess savant.
The Simpsons take a fun vacation at the newly "safe" Springfield beachfront area Mayor Quimby stated that the dangerous polluted water is not better in any way, it was only classified that after the safety standards were adjusted. Bart is left saddened by the failure of his "Bad to the Bone" tattoo, while Lisa finds a new sun hat which makes her relatively happy and wins her a lot of fans and admirers. However, Bart is not one of them; outraged with Lisa's good fortune and the tattoo, he throws her hat out the car window and it lands in a junk yard. When Lisa finds out that her hat is missing, she becomes inconsolable, and Bart feels more grotesque and gets uncomfortable visits from his "monster of guilty", a slime covered creature who sounds like Patton Oswalt and reminds him of the misdeed. Bart is unable to take the guilt anymore and tells Lisa the truth, and she promptly states it is "a wound that won't heal" refuses his desperate attempt to make amends with her. After a while Bart goes back to the junkyard and finds that the hat is now part of car cubed into trash. He uses a combination of Rod Flanders and Todd Flanders' Jesus-like powers and the acidity of Buzz Cola to break through the car and retrieve Sunny. However, when he gives the hat to Lisa, she rejects Sunny says that their relationships is over and he should just focus on Maggie ("give her raisins, Bart, she likes raisins") and he walks off. Lisa then has a emotional spirit vision of her own, telling her that he is trying to help her and she begins to sob and forgives Bart as they hug each other. The ending returns to the future-set opening where Lisa describes her ups and downs of Bart being a sibling, and lets the viewers realize Mrs. Muntz is dating a gaffer on this TV show.
Meanwhile, Homer is playing chess when Marge wants him to stop leering at women, and to the surprise of everyone especially himself turns out to be a grand master. Homer then remembers why he stopped playing: he and Abe bonded over chess after his mother Mona took off, but his father refused to continue playing after Homer beat him, and Homer thinks that his restored ability is an sign that he want to kill his father. Thanks to some great advice from the chess champion, Magnus Carlsen (who is apparently Carl Carlson's adoptive cousin), Homer and Abe play again and Homer lets Abe sort of healing a wound from the past. Homer wants to Skype with Carlsen again, but told by the Norgwin that he does not want to talk to him anymore.