Mark,
I have seen this before, and it is now your job to make a tough judgement call. The one question that needs to be answered, and that will determine your response, is to find out what she is really unhappy about. Some people will be unhappy with a portion of the job and just call the whole job bad, you need to engage her in a conversation to get to the real problem.
If she is being honest you should be able to isolate the problem and fix it. If she is not being honest and can only tell you that the whole thing is not good enough (you know the kind), then I would suggest that you consider walking away from it. Unfortunatly, there are people out there who make it their sole purpose in life to never be happy with any work that is done for them. Now, here is what you must decide. What will you charge her? Many here on the boards here will recommend that you negotiate a fair price after the work has been done, but whatever you do, never work for them again.
I always say, screw me once, shame on you. Screw me twice, shame on me.
If this were me and I suspected that they were being dishonest and just wanted a better price, I would not only walk away from future business with them but I would also hand them a zero dollar invoice. If I take full responsibility for the work (even though a case could be made for charging something) then they have no problem with me (of course, I would not advertise that I work for free!) because it cost them nothing.
If they do complain about everyone and everything, don't worry too much about who they tell. Those types of people are usually surrounded by others who know what they are like so when she starts talking bad about your business, the people she is telling will probably feel sorry for you having to deal with her!
One other point, I would point out that I do not believe that it is a good practice to routinely discount your prices after you have done the job if a customer is not satisfied. In fact, most customers are willing to pay your price - if the problems are fixed. So when they are unhappy, try to get to the root of the problem and fix it rather than just offering to discount your invoice. You will have a much happier customer on your hands.
The ONLY time that I ever consider reducing my invoice is if when we are finished the customer is honestly disappointed with the results. Not disappointed because of our work, but because of the item being washed just won't get any cleaner. In this case, I MAY consider knocking off just a bit to ease the disappointment a little. However, if they request that I reduce my invoice, I never do. That is just my style, you will need to decide what you are comfortable with doing.