You should ask for a refund, if for no other reason than to inform them politely that if one wishs to charge an hour to diagnose a waterpump noise, then one should get it right!
From the business side, this also is a calculated risk. One must charge for the time every car takes. As I pointed out before the entire business transaction: ticket write up, technician assignment, discussion of estimate, cashier, data entry, accounting costs a business the value of an hours labor. Notice I didn't include actually doing of anything to the car. As a result of these calculations a simple non invasive estimate should be charged for if the work not done.
But, I guarantee I have never charged anyone for a diagnosis on a water pump. If I have never seen you before I will do a walet biopsy first, before I waste valuable time on you. I will tell you that you have to leave the car!!!! I will tell you that it cost more than you want to pay and give you every opportunity to make an informed decision. And, after you have trusted me with your car I will do everything in my power to keep the costs of quality repair to a minimum and call with a exact cost before I start.
If I have to write two estimates for a person without doing any work, I will write no more. My time is too stretched to do all the work I do for hundreds of customers that have been with my company for tens of years. I say all this not to strut but to try and give you a feeling for the other side.
Bosch Master, ASE Master, L1
33 years MB technician