The screen is (if not 100%) then - let's say 97-99% - at a guess - scratch-resistant. Or; I've had my 1st gen Touch for over two years and it's bumped around in a bag with all kinds of scratchy things like keys, and still only have teeny-tiny, millimeter-short, non-noticeable scratches. It is not worth sacrificing clearness and sharpness of the screen to use a screen cover IMHO. There's a reason that most covers you can buy have no screen cover.
On the other hand, it might be a good idea to buy a cover for the body to protect it from falls to the floor etc. And if the backside cover is that high-polished metal finish, it'll collect scratches easily. If it's one of those sturdy silicone covers she has, I'd think it would be fine.
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