The costumer's umbrella is a light pink umbrella that belongs to Leone.
When Twinsen enters the pharmacy of Citadel Island and asks the pharmacist for a cure for his Dino-Fly, Leone says she can help him, but just as she is about to speak, her umbrella gets stolen by a thief. Twinsen then makes the deal with Leone, of recovering her umbrella in exchange on information about how to cure the Dino-Fly. Twinsen has sneak behind the thief and aproach him in discreet behaviour. Once confronted, he has to say "The umbrella please" so that the thief returns it to him.
After recovering it, Twinsen can give it to Leone, who says that he can go to the house of her employer, Ker'aooc the healer, to seek for help. Twinsen can also opt not to return the umbrella, and keep it. Later, in the Twinsonian souvenir shop in Otringal, he can sell the umbrella for 20 zlitos.
If Twinsen doesn't enter the pharmacy before the storm stops, none of these events occur.