The drink called Paintstripper has an ingredient something oily.
You can not fix the drink in the first act.
You will get some oil, eventually. Does The Establishment ? say anything to you?
Talk to Bartholomew about the business card to unlock The Establishment.
And you have entered The Establishment.
Did you become a member, so that you can enter the private spa?
Then Celestine gave you a welcome gift bag, didn't he? Open the bag by using it in the inventory and you will find a body oil.
That is your something oily. Put it into the hideous mug.