Kate & Leopold

In 1876, Leopold Alexis Elijah Walker Gareth Thomas Mountbatten, Duke of Albany and future inventor of the elevator, is a stifled dreamer. Strict Uncle Millard (Paxton Whitehead) has no patience for Leopold's disrespect for the monarchy, chastising him and telling him he must marry a rich American, as the Mountbatten family finances are depleted. His uncle has told him that on his "thirtieth birthday he had become a blemish to the family name".The Duke finds Stuart Besser (Liev Schreiber), an amateur physicist (and descendant of Leopold, according to deleted scenes) perusing his schematic diagrams and taking photographs of them. He had seen him earlier at Roebling's speech about the Brooklyn Bridge. Leopold follows Stuart and tries to save him from what he thinks is a suicide, falling after him into the portal that brought the man there in the first place.Leopold awakens in 21st century New York. He is at first confused and thinks that he has been kidnapped. Stuart says that he has created formulae to forecast portals in the temporal universe and that Leopold must stay inside his apartment until the portal opens again a week later. As Stuart takes his dog out, he is injured by falling into the elevator shaft, and is eventually institutionalized for speaking about his scientific discovery.Leopold is intrigued by the cynical and ambitious Kate McKay (Meg Ryan), Stuart's ex-girlfriend, who comes to the apartment for her Palm Pilot stylus. He observes that she is a "career woman" and that her field, market research, is a fine avocation for a woman and states that he once dated a librarian from Sussex. Kate dismisses him and demands that he take Stuart's dog for a walk. Leopold is overwhelmed to see that Roebling's bridge is still standing. Back at the apartment, he befriends Charlie (Breckin Meyer), Kate's brother and an actor between gigs, who believes him to be an actor as well, steadfast to his character.Kate and Leopold become romantically involved, as they dine and tour New York.When shooting begins on the commercial in which Leopold has agreed to act, he finds the product, diet margarine, disgusting. He cannot understand how Kate would have him endorse a flawed item without qualms, and declares that "when someone is involved in something entirely without merit, one withdraws". Echoing his uncle, Kate says that sometimes one has to do things they don't want to. He chides her about integrity. She retorts, "I don't have time for pious speeches from two hundred year old men who have not worked a day in their life". Their dalliance seems at an end.Stuart escapes from the mental hospital, and while Kate is accepting her promotion at a company banquet, he and Charlie are racing to meet her. Moments before she goes on stage, they arrive and produce pictures from Stuart's camera that show her in 1876. Stuart says that he had thought he disrupted the spacetime continuum, but actually "the whole thing is a beautiful 4-D pretzel of kismetic inevitability".Kate chooses a life with Leopold over her career, and the three of them escape to the Brooklyn Bridge. There, catching the portal before it closes, Kate vanishes into 1876 where Leopold is himself about to announce Miss Tree as his bride. As he opens his mouth to speak, he sees Kate and announces her name, Kate McKay, as his bride.In the closing scene, they kiss and the camera is drawn outward showing a wall clock depicting 12:15.

Question: What does Kate come to Stuart's apartment to retrieve?
Answer: Stylus