Rejecting a settlement letter could either lead to further negotiations or to a courtroom trial where you seek a jury award for your losses. 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. Considering rejecting an insurance offer? Here's how it can impact your claim. I wish to file an appeal concerning. If you disagree with the offer, you can decline it. However, rejecting a settlement offer isn't as simple as saying, "Sorry, I won't accept it." It is in your best interest to document your counteroffer in writing and send it to the insurance claims adjuster. Request to begin debt settlement negotiations.