Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone.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." The insurer's refusal to settle a case is not unlimited. I crafted a demand letter, from a combination of many templates I found online. If you decide to reject the settlement offer, you'll need to do so in writing.