Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Rejecting a settlement letter could either lead to further negotiations or to a courtroom trial where you seek a jury award for your losses.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." This article will explain how to write the best demand letter to a Georgia insurance adjuster. For this reason, never accept a settlement offer from the insurance company without first reviewing it with your car accident attorney. Rejecting Your Demands. For this reason, never accept a settlement offer from the insurance company without first reviewing it with your car accident attorney. Rejecting Your Demands. Atlanta Wrongful Death.