Before rejecting the offer outright, it is important to carefully evaluate it. Sample Rejection Letter for a Low Settlement Offer.This is a sample letter seeking a reduction in a medical lien. 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. I wish to file an appeal concerning. A settlement negotiation begins with one side making a demand or an offer. This initial amount is generally much higher or lower than the claim is worth. Annual costs up to three (3) years of service. 8. Larger medical bills tend to lead to larger settlements.