By the use of a shipping restrictor app, such as Easy Shipping Restrictions you can block orders from coming in from a particular ZIP/Postal code. They offer a 3 day trial and from there on it's $4 per month. What you could do is use it for one month and hopefully, that will deter the customer from making further attempts. If they come back, you can install it again.
If there is anything else I can help you with, please let me know.