The body of the letter will depend upon whether you're accepting or denying their claim. In either case, it doesn't hurt to open with:
Thank you for your (letter/comment/whatever) of (date). ABC Company is constantly striving to improve customer service, and we could not do that without the valuable input from people like you.
In regards to your complaint.....(insert your findings here, are you going to refund their money, or are they out of luck).
We thank you again for your input, and hope to be of service to you in the future.