Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. In this article, find out the proper way to do this.Victims who want to respond to a low settlement demand offer must use factual information, persuasive arguments, and a professional tone. Sample Counteroffer Letter for Your Insurance Settlement Negotiation. Here's an example of a counteroffer letter you can use to draft your own.