Considering rejecting an insurance offer? Here's how it can impact your claim.Remain calm and professional when responding to a low personal injury settlement offer. You can reject it and renegotiate. Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Find out what happens if you refuse a settlement offer and how a personal injury lawyer can assist you in fighting for fair compensation. We recommend that you reject the offer in writing rather than over the phone. You can and should challenge the offer you receive with the aid of an experienced personal injury lawyer. Settlement can be the fastest, easiest and most fair option for an injured party because of all of the time it takes for investigation, prelitigation and trial. 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.