The Talented Mr. Ripley

Tom Ripley is a young man struggling to make a living in 1950s New York City. While playing piano at a cocktail party in New York City, he is approached by wealthy shipbuilder Herbert Greenleaf, who mistakenly believes that Ripley went to Princeton University with his son, Dickie, because Ripley is wearing a borrowed Princeton blazer. Greenleaf recruits Ripley to travel to Italy and persuade Dickie to return to the United States, for which he will pay Ripley $1,000 (equivalent to $8,834 in 2015). Ripley accepts the proposal, even though he did not attend Princeton and has never met Dickie.
Upon arriving by ship in Europe, Ripley meets a wealthy textile heiress named Meredith Logue. During their brief conversation, he impulsively pretends to be Dickie, later commenting in voice-over that "it is better to be a fake somebody than a real nobody." Shortly after his arrival in Italy, Ripley fakes a chance encounter on the beach with Dickie and his fiancÃ©e, Marge Sherwood. Ripley later discloses to Dickie and Marge that Mr. Greenleaf paid him to travel to Europe and persuade Dickie to return home. This revelation infuriates Dickie; he declines the invitation and suggests Ripley go back to America and inform his father that he has no intention of ever returning. Ripley instead ingratiates himself into Dickie's life under the pretext of being a fellow jazz lover. The two concoct a scheme for Ripley to wring additional funds from Greenleaf by regularly mailing letters suggesting Dickie is wavering and will likely return to America if Ripley can remain in Italy and continue applying pressure.
On a jaunt to Rome, Ripley meets Dickie's friend Freddie Miles, who treats Ripley with barely concealed contempt. A local girl, pregnant by Dickie, drowns herself after he refuses to help her financially; this sends Dickie into a downward spiral. He begins tiring of Ripley, resenting his constant presence and suffocating dependence. Ripley's own feelings are complicated by his desire to maintain the opulent lifestyle Dickie has afforded him, and his growing sexual obsession with his new friend. As a good-will gesture before Ripley returns to America, Dickie invites Ripley to sail with him for a last trip to Sanremo, where Dickie is looking to relocate. While at sea, Ripley suggests he return to Italy the following year and the two become housemates. Dickie dismisses Ripley's idea, telling Ripley that he intends to marry Marge and admitting he has grown weary of Ripley. Upset by this news, Ripley confronts Dickie about his behavior and lashes out in rage, repeatedly hitting Dickie with an oar, killing him. To conceal the murder, Ripley scuttles the boat with Dickie's body aboard before swimming ashore.
When the hotel concierge mistakes Ripley for Dickie, he realizes he can assume Dickie's identity. He forges Dickie's signature and begins living off Dickie's trust fund. He uses Dickie's typewriter to communicate with Marge, making her believe that Dickie has left her and has decided to stay in Rome. He checks into two separate hotels as himself and as Dickie, passing messages via the hotel staff to create the illusion that Dickie is still alive. His situation is complicated by the reappearance of Meredith, who still believes that he is Dickie.
Ripley rents a large apartment and spends an isolated Christmas buying himself expensive presents. Freddie tracks Ripley to his apartment in Rome through the American Express office, expecting to find Dickie. Freddie is immediately suspicious of Ripley as the apartment is not furnished in Dickie's style, while Ripley appears to have adopted Dickie's hair-style and mannerisms. On his way out, Freddie encounters the building's landlady who refers to Ripley as "Signor Dickie". Suspicious, Freddie goes back to confront Ripley, who murders him. Ripley carries the body to Freddie's car and abandons both in the woods.
Investigating the murder, the Italian police come looking for "Dickie" but find Ripley, who subtly implicates Dickie. Ripley eludes imminent capture and clears himself by forging a suicide note addressed to Ripley in Dickie's name. He then moves to Venice and rents an apartment under his real name. Though trusted by Dickie's father, Ripley is disquieted when Greenleaf hires American private detective Alvin MacCarron to investigate Dickie's disappearance. Marge suspects Ripley's involvement in Dickie's death and confronts him after finding Dickie's rings in Ripley's bathroom. Ripley appears poised to murder Marge but is interrupted when Peter Smith-Kingsley, a mutual friend, enters the apartment with a key Ripley had given him.
MacCarron, after uncovering certain sordid details about Dickie's past, reveals to Ripley that Greenleaf has requested the investigation be dropped. MacCarron will not share his revelations with the Italian police and asks Ripley to promise to do the same. In exchange for his candor, and implications made in Dickie's suicide note, Greenleaf intends to transfer a substantial portion of Dickie's trust fund income to Ripley. Dismayed at the resolution, Marge furiously accuses Ripley of involvement in Dickie's disappearance before Greenleaf and MacCarron drag her away.
Ripley and Peter, now lovers, go on a cruise together, and Ripley discovers that Meredith is also on board. She has spotted Peter, an old acquaintance; this endangers Ripley's deception, but he cannot murder Meredith because she is accompanied by her family. Ripley goes to Peter's cabin and suggests that they remain below deck for the duration of the cruise. He quickly dismisses this idea as he cannot offer Peter a legitimate reason for doing so, and mournfully strangles Peter to death before returning to his own cabin.

Question: What does Marge find in Ripley's bathroom, leading to her confronting him?
Answer: Dickie's rings