Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone. This article delves into the complexities of such a decision, the subsequent steps, and the importance of informed legal guidance throughout the process.Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. What Are the Potential Responses to a Demand Letter? Take it up a notch and set a deadline for the insurance company to accept your offer in the demand letter. You can and should challenge the offer you receive with the aid of an experienced personal injury lawyer. I wish to file an appeal concerning. It may pay to reject a settlement offer you receive from an insurance company after an accident. RULE 20-205 - NOTICE OF REFUSAL TO PROBATE REJECTED WILL OR. SAN BERNARDINO County.