Learn how to write a medical bill dispute letter and avoid paying more than you need to for medical procedures. Remain calm and professional when responding to a low personal injury settlement offer.You can reject it and renegotiate. Considering rejecting an insurance offer? Here's how it can impact your claim. Refusing a settlement offer is normal. 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. Get more tips on writing a winning demand letter. And check out our sample demand letters to get an idea of what this kind of correspondence might look like:.