Near the beginning of the story, Muriel complains to her mother that Seymour refuses to take his bathrobe off, which she flippantly attributes to him wanting to hide his pale complexion. However, his bizarre attachment to the bathrobe actually symbolizes how he closes himself off to other adults and the adult world they inhabit. Indeed, when the story introduces Seymour a few pages later, he’s lying on the beach with his eyes closed, but he’s bundled up in his robe. When Sybil walks up and startles him, Seymour’s hand instinctively flies up to the lapels of his robe, as if he were closing it tighter and closing himself off from the interaction. But when Seymour notices that the visitor is a child, he relaxes, and it’s not long before he takes off his robe entirely to go swimming with her. That Seymour so willingly sheds his robe, which appears to be a kind of security blanket for him, reveals that he’s much more comfortable with children than adults, and it points to the thematic idea that he is drawn to the innocence that children represent. True to form, when Seymour leaves Sybil’s company and walks back to his hotel, he puts his robe back on and “close[s] the lapels tight,” closing himself back up both physically and emotionally as he prepares to reenter the adult world.
More specifically, it seems that the bathrobe symbolizes Seymour’s attempt to conceal his wartime experiences—and resulting psychological trauma—from others. After first writing off Seymour’s behavior as simple embarrassment about his pasty skin, Muriel eventually admits to her mother that Seymour wears the bathrobe so that people don’t stare at his tattoo. Surprised, her mother asks if Seymour got a tattoo in the army, and Muriel says no—he doesn’t have a tattoo. With this, the story implies that this invisible tattoo that Seymour is desperate to cover up is a stand-in for Seymour’s experiences in World War II. He worries that people will see these experiences—and his subsequent psychological trauma—just by looking at him, and so bundling himself up in the bathrobe is a way for him to close himself off from other people.