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.Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone. Instead, you have to write a formal letter rejecting the settlement. If you disagree with the offer, you can decline it. However, rejecting a settlement offer isn't as simple as saying, "Sorry, I won't accept it." In this article, find out the proper way to do this. Get tips on how long you can consider a settlement offer and what to evaluate before accepting. Speak to an attorney for guidance. The letter begins the negotiations to settle your personal injury claim.