Faulty replacement iPhone 5? - 1

The scenario is that my grandma and grandad went halves to buy me this iPhone 5 for Christmas but they let me have it as soon as it arrived in November as my contract at the time was approaching end.
Anyway, as soon as I got it set up, I noticed a battery draining issue. I tried it for a few weeks and even one night where I needed it I had no battery and I'd hardly used it.

We took it to the Apple Store where the guy did a deeper software reset, that made no difference and so it went back this Saturday just gone.
It was about 24 hours after the exchange happened, I was looking at an album on the iTunes Store and was contemplating whether to but it or not, when I saw like a scratch, but I hadn't dropped it or scratched it, and so I looked carefully and found a few dead pixels.

I've just done a test online and there are quite a few dead pixels around the screen.

I only notice the first few if I look carefully, but because I know it's there, it bothers me and it bothers me that my grandparents have spent £599 on nothing but troubled iPhones

I have another Genius Bar appointment booked for Sunday, what will they more than likely do?

Added (1). @John - Thanks for your answers. Although what I've got isn't a scratch, it is just numerous dead pixels around the screen. I do have a case for it and it is well protected. I just feel how we've spent so much money on it, then it deserves to be perfect

You could try to explain it to them that would help!
Or just hide the scratch from them!
But, Always make sure you have a back cover on it and a screen protector this really does help you!

I know someone who scratched there phone once but, there parents have never noticed!
But, whenever you get a phone ALWAYS AND I MEAN ALWAYS get cover on it so when you drop it OR SCRATCH it! - you can get a brand new one free!
But, Don't Worry!
That's all I can give you I'm afraid!

I would go to your appointment and see what they can do. If they won't do it for free i would use apple tree's services. They are cheaper than apple and do free shipping anywhere in the UK and claim to be the cheapest in the UK. I will post the link below