That being said, unless you have a witness or it in writing, you have no chance of winning as it will be based on hearsay and conjecture. If he raises a Paypal complaint you have less than no hope as their complaints are 90% automated with "non-physical" items being directly excluded from their Terms Of Service. Paypal very much works on a "first to complain wins" basis for non-physical items.

Your interpretation of Paypal's dispute resolution process is completely inaccurate. In fact, it's the complete opposite.

@Matt - I see that this happened a few weeks ago so I'm not sure if it ever went to dispute or not. In any event, Paypal will typically side with a seller 9 times out 10, when it involves virtual/intangible goods. So, whether you even have a "contract" or not isn't the issue as far as PayPal is concerned. They have no desire to be in the business of reading third party contracts. You should win this so long as you make it clear to PayPal that you delivered SOMETHING for the buyer's payment to you. That is the key here. You must show reasonable "proof" that you completed AND delivered a design. This can prove difficult when it involves intangibles, which is why they typically take the seller's side, regardless whether it's to the client's satisfaction or not.

If it falls to dispute, then I'd recommend uploading screenshots of the time stamps of the email that had the attached mockup and upload the mockup itself, during the dispute. I would also include any other "evidence" that may support your case, such as other emails, ip address, specific links, forum threads, etc. I know it sounds harsh, but sadly Paypal isn't interested in whether your client was happy with an intangible service. They just want to make sure he received something. With paypal being the most popular payment processor for virtual services, can you imagine how many disgruntled web hosting clients paypal has to deal with on a daily basis? Exactly. This is why they don't typically like to side with the buyers of virtual goods in most cases. It's too messy. There are strong cases where the buyer wins, but that is not nearly as prevalent. That being said, if they suspect that you are committing fraud by not delivering a service for payment, then they will return the money to the buyer and either freeze your account, or closely monitor you from that point forward. That is the standard treatment given to real fraudsters who coincidentally are terrible communicators more often than not. Paypal hasn't grown to the size they are by being stupid and clueless.

There are two exceptions to the above:

1.) Was your client's payment made with paypal funds, or a credit card via paypal? If the later, then you can kiss your money, mockup and time goodbye if he ultimately requests a chargeback directly with his bank/credit card company.

2.) The only downside to what you've stated above, is that you already offered to return half of your client's payment. From Paypal's perspective, this will automatically signify some type of "fault" on your behalf, to some degree, and you can be sure that your client will use those emails to his favor. So at this point, I'm not sure if paypal will actually return 50% of his money if you "win". They typically are "all or nothing" when it comes to payments; otherwise their job becomes too complicated. My advice is that if this ever happens in the future, stand by your terms when you get a client who acts up. Don't play so nice. It's your time and talent. This is business. No refunds should ever be given to a client after they have your design, software, or logo in their possession or your service has been completed. Otherwise it is theft since it's virtually impossible to "return" these "items".

I was in the freelance web design business for over 10 years and have had to deal with a few random clients attempting to steal my designs and logos, so I am very familiar with how this process works. Now, tangible items are a whole different can of worms.