The Canon Warranty Card is useless. Check and see if the dealer from which you purchased the lens is a Canon Authorized Retailer. That is the only time Canon will do warranty work on a Canon item.
They want to see the invoice from the authorized dealer in order to provide warranty work. They could care less about the waranty card. What the earlier posting alluded to was that Canon "MAY" do warranty work on a gray market iutem which was purchased from a Canon Authorized Dealer.
An example of a Canon Authorized Dealer that sells both Canon USA and Canon Gray Market items is B&H in New York City. This company is extremely honest and clearly states when an item they are selling is grey market.
I strongly suspect that the item you purchased is NOT covered by the Canon USA warranty. It may not even have been new. Lots of sales on the internet advertise items as "NEW" when the correct terminology is :"IN LIKE-NEW CONDITION". The reason I suspect that your dealer is unscrupulous is that a Canon Authorized Dealer would have told you, "Don't worry, you don't need the warranty card. Our invoice is all you need for waranty work!"
On the positive side, most times that I have needed warranty work done is early after my purchase. If a camera works perfectly at the start, it will often work well through the warranty period. In fact, I now have no qualms about purchasing a Canon Refurbished Item which has only a 90-day warranty. However, I would be hesitant to pruchase an item without any warranty unless I was paying a used item price.
I also hesitate to purchase through Adorama vendors unless I am familiar with the vendor. However, I have no worries about purchasing from Adorama Direct. If you have problems with the vendor misrepresenting the status of the item and if the dealer will not satisfy you; I would go to Adorama. I feel that Adorama has a fiduciary responsibility to ensure hat vendors selling on their site describe the items accurately.