I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
First of all, your 4 year warranty is long since passed and it cannot be extended without your approval. Only if you have been given notice of the need for repairs under the warranty before the 4 years passed, would you have any liability to do the repairs.
As for the death of the original owner, your contract was with the owner of the home and not with their granddaughter. The granddaughter has no legal right to enforce the contract you made with the property owner----unless your warranty specifically stated that it was transferable to a subsequent owner---and even then the daughter would have to show that she now owns the property AND that the warranty is still active---which it clearly is not.
Feel free to ignore the granddaughter's demand, and let her try to make a claim against your bond. The claim will go nowhere because the warranty is no longer in existence for that property.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best in 2016,