In my opinion, the Duchess does this to try to distract Oliver Bacon and to make him more likely to accept her "jewels" and pay a high price for them.
The Duchess is really in a desperate situation and needs the money badly. She knows her pearls are fake but she needs a high price for them. She knows that Oliver wants to be included in high society -- to be seen as an equal to people like her.
So as he inspects the pearls, she invites him to spend a long weekend at her place. She hopes (and gets her wish) that this will really appeal to him and he will not inspect the pearls too closely.