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 decide to reject the settlement offer, you'll need to do so in writing. 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." To reject the initial offer, you will create a counteroffer and send it via mail to the insurance company claims adjuster. Can a lawyer sign an out of court settlement on behalf of a client and refuse to show the client the actual settlement agreement? You can and should challenge the offer you receive with the aid of an experienced personal injury lawyer.