This letter should clearly state the reasons for rejecting the offer, such as it not providing maximum compensation for the damages incurred. Looking for a sample nonengagement letter?We've created a guide to non-representation letters and also included a sample letter. Understand your options when the insurance company makes a lowball injury settlement offer, and see a claimant's sample response letter. Sample Counteroffer Letter for Your Insurance Settlement Negotiation. Here's an example of a counteroffer letter you can use to draft your own. Attorneys will make no settlement of clients' claims without clients' consent. You should first submit a letter that outlines your refusal. We recommend that you reject the offer in writing rather than over the phone. An attorney can also draft this letter for you, making sure it covers all the bases for your dog bite claim.