Before changing targeting, establish three numbers: speed to first contact, number of contact attempts, and the percentage of leads with a documented disposition. In our experience, when a client complains about lead quality, at least one of those three is broken more often than the targeting is.
That is not a defence of bad leads. Cheap leads are easy to generate and a real failure mode. It is a sequencing argument: you cannot diagnose the top of the funnel while the middle is leaking, and changing targeting first destroys the only baseline you had.
The uncomfortable version of this conversation with a client is worth having early. "We will improve lead quality and you will improve speed to lead, and we will both report on our half" is a partnership. Absorbing the complaint silently is how a retainer dies quietly.