Believe it or not, everyone who works at the dealership service department may not have in depth knowledge of how every component on the car behaves. It's unfortunate they kept your car for so long and did unnecessary work before doing research, but the fact of the matter is there is nothing wrong with your car. The clicking goes away after a minute or two of running.
I will give a little anecdote about my last car. I brought my Golf GTI in to VW because it was feeling sluggish when the temperature was cold and down on power. 3 times i brought it in and 3 times they failed to diagnose the problem correctly. And yes I had to pay for each one of those misdiagnoses. I finally figured out it was the rear PCV valve sticking when cold. If they simply looked at a schematic of that system like I eventually did, they should have been able to figure it out. In short, people in service departments may be minimally trained with the exception of doing step by step repeatable tasks. It varies by dealership, so find a good one that hires quality mechanics and technicians if you can.
