If you call the apple helpline, they should be able to tell you. They do give out replacement headphones at times, (given a valid reason), so I don't see why they wouldn't for the remote if within the warranty.
If you have Applecare, or are within your one year warranty service, you can get it replaced. You can fill out a form to get this replaced on the internet at Apples site if you they won't talk to you on the phone.
My remote worked for a few months then started adding static - I think it was a loose connection. I called AppleCare and they sent me a new one - I received it the next day.