Of course this should be fixed on their dime but expect a butt load of hassle and tons of denial and claims that you were juggling fire lit chain saws in your car while smoking.
Also if they do decide to fix it expect your car to be gone for like a month and for **** to go wrong after since i'm sure you're well aware, pulling out the main carpet of a car is no joke and will require them to pull out almost everything on the bottom end of your car and probably not put it back properly while destroying all your push clips while they do and and not replace those.
That's exactly why I'm annoyed. I know it's no small thing that requires you to basically strip the car down to replace, but it's something that's really noticeable and can cause problems with the carpeting in the long run. If there's a flooring patch or some way to fix it without ripping it all up, I'd be okay with that. Still very annoyed since the flooring had no issues when I brought it in, but at least it would be tolerable.
It's annoying as hell that all this is being messed up on the car since it's not even a year old, I've babied it since I bought it, and none of the problems have been cause by me.
If it's easily hidden, I wouldn't bother with it. Like evo said, it'll cause more trouble than it's worth.
If it was something that could be covered by the floor mat, I'd totally be in the same boat, but it's outside the mat. Hopefully they can fuse it or sew it or something to repair it. I just don't want it tearing on me further.