How do I get a refund of an iTunes gift card with illegible numbers for redeeming the value?
I was in this situation once. However I went to the Apple support site, followed what they said, and then filled out the email form. From what I remember they will ask you for what you can make out of the code, and then the serial number of the gift card. 
This is the link to the email form submission page: http://www.apple.com/support/itunes/contact.html?form=cards_codes&amp;topic=iTunes%20Cards%20and%20Codes&amp;subtopic=Redemption%20questions
Where it says 'specific request' select 'my code is scratched or unreadable.' Proceed to fill in the form as best you can and send it off. I got a response in less that 48 hours, and the answer they gave me allowed me to redeem my card.
In answer to your original question, I don't actually know, but I hope this assistance means you will no longer have a need to refund the card. Hope this helps.