Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Gather Evidence: You'll need evidence to justify rejecting the settlement offer.Instead, you have to write a formal letter rejecting the settlement. Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone. In this article, find out the proper way to do this. On the other hand, reasons for rejecting a settlement offer include: The company denied your settlement offer without justifying the denial. If a settlement is offered, you reserve the right to reject and counter. David L. Engelsher practices in the area of personal injury law. By comparison, in the case of a structured settlement, the plaintiff and the defense agree to settle the physical injury claim in exchange for the defendant's. For example, you might file an insurance claim after a car accident to get coverage for vehicle damages and medical bills.