How to remove scratches on the back of my iphone 5c?

Ok so my iPhone is my baby and I take really good care of it. I think when I took one of my cases or lenses of I scratched it and it really bothers me and makes me really nervous. Could you please help because ik I sound spoiled but I make a big deal about this because you know iPhones aren't exactly "cheap".

If it is plastic this works
http://www.amazon.com/...0014R9V9O/

It worked well on my plastic watch crystal