The letter should state/quote the relevant terms of the contract and that the contract was breached (and how--i.e. by not completing the work in time) and accordingly ask for the refund (i.e. for the amount you deem appropriate).
If they will not agree to refund an acceptable amount to you (they may offer less than you want, but it may be worth taking to avoid litigation; see below), you will have to sue for the money. You would sue based on "breach of contract," or violating the terms of the agreement.
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