No peace for the wicked means that someone's heavy workload or lack of tranquillity is punishment for a sinful life, and here the folks were staring at the speaker vengefully because of their bad actions and not because they have done something good.
Consider the statement "After the pleasantries were over, they started on me with a vengeance, which is what people who have done something good deserve.". Based on this "After the pleasantries were over, they started on me with a vengeance, no peace for the wicked." a true statement? Yes, no, or I don't know?