Why don't you just put a thin TPU case on there? Won't add much bulk and will prevent further damage. Diztronic makes a good one for $10 on Amazon, and it will likely cover the damaged part.
As for repair, you'd have to contact Samsung unless somebody else here has had the same experience.
Was it dropped? How so and from what height? Just wondering what kind of fall that screen survived.
You could send in for repair but god knows how much they would charge for it. I second the case idea, unless its just driving you that crazy
Sent from my DROID RAZR HD using Xparent Cyan Tapatalk 2
"She leans into me and I keep my arms around her. I don't fool myself that I hold her together -- She does that on her own -- But holding her keeps me from flying apart."
I'm sure there is a way to get a replacement part but it'd most likely require you having to take the whole phone apart, which isn't a particularly simple process.
At this point I agree with Brian. I used to use that same case and it's awesome. Keeps the phone from being too slippery, covers the corners, and super thin. Good luck.
Amazon.com: Diztronic Matte Back Dark Blue Flexible TPU Case & Screen Protector for Samsung Galaxy S III (Sprint, AT&T, T-Mobile, US Cellular, Verizon) [Diztronic Retail Packaging]: Cell Phones & Accessories
Well if it helps I did that once at about the same height with my Rezound, shattered the screen to the point it didn't work after a few days. So I guess the S3 screen IS stronger than this forum would lead you to believe...