To answer this question, it is important to realize that in the short story "The Duchess and the Jeweller" by Virginia Woolf, the author uses the first part of the story giving the backstory of Oliver Bacon, the jeweler. His skill at his trade has taken him from a childhood of stealing dogs and selling them in dark alleyways to being "the greatest jeweller in the whole world." Rich and aristocratic people come to him because they trust his reputation. He would easily be able to tell the difference between real and fake jewelry.
On the day the story takes place, the Duchess of Lambourne, a woman from an old aristocratic family, comes to him with pearls to sell. She has been gambling again and has to pay off debts so that her husband will not find out. However, more is involved in this transaction than pearls. Mr. Bacon, the jeweler, is in love with Diana, one of the duchess's daughters. This all sets up the situation so that we can answer the question.
The pearls that the duchess brings to sell to the jeweler are fakes. Mr. Bacon wonders, "Is she lying again?" This suggests that she has brought him fake jewelry in the past. He realizes that he should have the pearls tested to find out for sure if they are real or not. As if sensing his uncertainty, the duchess then invites him for a long weekend at which Diana will be present. At this point, the jeweler doesn't care about the authenticity of the pearls. He writes the check not so much to acquire the pearls as to help out Diana's mother. So the duchess cheats Mr. Bacon by selling him fake pearls. After she leaves, he quickly discovers that they are fakes, but he reacts positively. He has spent a large amount of money for worthless trinkets, but in exchange he has gained the goodwill of Diana's mother and a long weekend with the woman he loves.