I think that the receipt helps speed up processing, but that it's not necessary. You can still register your product using the serial number and part number on the card. Your past order should also be visible in Amazon, to take a screenshot of.
I think that you should have no problem applying for the thermal pads without an invoice, so long as you register your card with EVGA (which doesn't require an invoice to be uploaded). However, in the worst-case scenario, it would cost you only $5 or so to buy the needed thermal pads, yourself. But I think you're fine. Just register your card with EVGA, and apply for the thermal pad mod at the bottom of this page:
http://www.evga.com/thermalmod/