Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Upon rejecting an initial settlement offer, the next step involves drafting and presenting a counteroffer.Your counteroffer likely demands a higher sum. To reject the initial offer, you will create a counteroffer and send it via mail to the insurance company claims adjuster. Always reject a settlement offer in writing. Type a letter to your contact at the insurance company listing the reasons you think that their offer is too low. Learn how to write a letter of appeal for insurance claim rejections in eight easy steps. The letter should be addressed to the name of the appeals analyst referenced in the denial letter. It should be sent certified mail, return receipt requested. Instead, you have to write a formal letter rejecting the settlement.