Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Remain calm and professional when responding to a low personal injury settlement offer.You can reject it and renegotiate. If you decide to reject the settlement offer, you'll need to do so in writing. Crafting a demand letter requires two critical steps: working out the worth of your claim and ensuring that you have all the evidence to back it up.