It is not correct to use "the." We use "a" in this case because we are talking about a common customer. There is no specific customer implied. Even if you were already talking about customers in your material, there is not a specific customer who has booked you. Also, your sentence reads like the title of something, which I feel should use "a." For example in an airplane safety manual: "In this section we will cover what to do in case of an emergency water landing." "a" water landing--the kind that can happen in all bodies of water.
If there was a specific customer, then the sentence would read thus: "...what other service providers had to say about the customer who booked you."
This assumes that your example comes from some sort of training material and not an employee review.