The mango, spray-painted with gold and left for the cabin while they were at archery practice, bore the phrase "For the hottest." The Aphrodite cabin, after fighting meaninglessly over the proper recipient of the mango, got revenge on the Stoll brothers by applying Permanent Makeup to Travis, and cursing Connor so that all of his clothes would be two sizes too small.
The trick is a reference to the mythological Judgement of Paris, the event that set in motion the Trojan War. Eris, the goddess of chaos, was not invited to the wedding of divine Thetis and Peleus because her presence would have cursed the happy event. Enraged, she exacted revenge by throwing her golden Apple of Discord into the assembly. On it was written the Greek phrase Kallisti, or "to the fairest one," and all the goddesses present began to fight over the proper owner of the apple. Eventually the contest was narrowed to Hera, Athena, and Aphrodite. The duty to judge fell to Zeus, but knowing his decision would cause chaos among the gods he chose the mortal prince Paris to make the decision instead.
Paris, prince of Troy, was brought to Olympus to choose between the three goddesses, but each was so peerless in beauty that he couldn't make a judgement. Therefore each offered Paris a bribe. Hera, as Queen of the Gods, could have made him king of the mortal world. Athena, goddess of wisdom, bribed him with great wisdom and skill in warfare. Aphrodite, however, offered him the love of the most beautiful woman in the world. Hearing that, Paris instantly chose Aphrodite as the fairest goddess, earning him the hatred of Hera and Athena. His prize was the gorgeous Helen, incidentally a married woman. Her husband was Meneleus, king of Sparta, who would lead an alliance of Greek forces against the city of Troy to reclaim her.