This is where having a portfolio of before and after pictures and some informative literature can really help you out and help the customer make a more informed decision. Of course, this type of customer may be completely happy with a a simple polish and wax and only willing to pay for that and not spring for a complete paint correction.
When you are speaking with your customer about paint correction, focus on positive words to describe what you can offer. Talk about the clear, shiny finish with maximum gloss that results from polishing. Using the words compound and compounding may be scaring them and more often than not, you won't even need to use a compound so work on your presentation to focus on the positive and stay away from words that may trigger discomfort. Put the customer at ease with your confidence in your skills and ability.
As a detailing business owner not only are you a technician, but you are also a salesman. If their vehicle has paint defects and you can fix it, they need your service if they want their car to look it's best but due to the fear they have of removing paint, they may not want it. Someone is going to get sold here. Either they are going to sell you on the idea that they are too scared of machine polishing or you are going to sell them on the idea that you are the right person to care for their care, make it look as good as it possibly can look and do it safely with no reason to worry.
If you really want to convince a skeptical customer, be armed with a
paint thickness gauge and offer a free test spot to show that the paint look so much better and they still have plenty of paint actually on the car too!