Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. You or your personal injury lawyer will need to draft a formal business letter that makes a case for your counteroffer.Remain calm and professional when responding to a low personal injury settlement offer. You can reject it and renegotiate. A demand letter explains why you deserve compensation for your injuries and damages from an atfault party after an accident. Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone. Follow up letters with phone calls and document whom you speak to. After careful consideration, I must reject this offer as it does not meet my needs based on the severity and ongoing nature of my injuries. A demand letter explains why you deserve compensation for your injuries and damages from an atfault party after an accident. Provide a clear explanation of why you are rejecting the offer and include any supporting evidence that backs up your position.