I'd go to the Service Manager yourself with your account in hand, and express your doubts that the belt was replaced, and explain the logic of your reasons. Be very civil, as this is just the first port of call, and it might get sorted there and then.
If you don't want them to do the job after being gypped, suggest that a refund would be appropriate.
If they dig in, then you mention to the Service Manager that you intend to now make a formal complaint to Hyundai. He won't let on, but he'll be crapping himself, because the dealer's contract with the factory will be to trade ethically, and not endanger the good name of Hyundai.
Make a phone call to Hyundai and ask to speak to the Customer Service Manager, or someone high up, and explain what happened. Always be polite and you'll be amazed how people respond. Try to avoid the clerical level, as they just pass it up the line.
Other than the first service, I never ever go near the dealer again. You just get an apprentice doing the work, but pay top dollar. Try and pick out a reliable local workshop who is often half the price of a dealer, and their stamp in the service book does not void your warranty, by law.
Let us know how you go, and there's more if need be.