Remain calm and professional when responding to a low personal injury settlement offer. You can reject it and renegotiate.Assume you sent a demand letter for, let's say, money owed. Respondent, predictably, doesn't respond. Under Texas Rule of Civil Procedure 167, if an offer of settlement is made in accordance with the rule, then certain litigation costs can be awarded. Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Rejecting an initial offer does not mean the end of settlement negotiations. Instead, it's a common step in a longer process. I looked back at some rejection letters I sent and realized that I usually follow a pretty simple format: Say thanks. The first step in rejecting a low settlement offer is to write a letter to the insurance company stating the rejection.