In Act IV, Joseph tries to convince Sir Peter that the woman behind the screen is just a French milliner in order to distract Sir Peter from his suspicions about Lady Teazle.
Sir Peter, already suspicious of his wife’s behavior, has been led to believe that she may be having an affair with Joseph. When Sir Peter sees the woman hiding behind the screen, Joseph seizes the opportunity to provide a plausible excuse, claiming she is simply a milliner, in order to steer Sir Peter's focus away from the more troubling possibility—that it is his wife, Lady Teazle, who is behind the screen.
Joseph’s motivation is to calm Sir Peter's suspicions and prevent any immediate confrontation or drama that might arise from the situation.
By convincing Sir Peter of a harmless explanation, he buys time to protect his own interests and keep the situation from escalating.
