Your job is to insulate your team from the normal course of business (customer negotiating) so that they don't feel like it's "insanely disrespectful." Your job

Your job is to insulate your team from the normal course of business (customer negotiating) so that they don't feel like it's "insanely disrespectful." Your job is to process it unemotionally and handle it unemotionally. Let the customer say whatever the customer is going to say and then respond with a boilerplate like "We've considered these possibilities and appreciate the input but we are not flexible on our original estimate."