Greasy fingers...

I just recently purchased an Iphone. After heavy usage for an entire day I found it was easy to remove a days worth of smudge from the screen with the cloth. However, when my wife uses it, even for less then 1 minute, I notice the screen actually has what feels like a layer of dirt and residue on the screen. This residue is extremely difficult to clean off. you can also feel your fingers rubbing over it, kinda ruining that sleek smooth touch experience.

My wife is getting her Iphone next week but I'm a bit concerned about the residue her fingers leave. If 1 minute leaves residue as described, what is gonna happen after a full days use? Her hands are very clean and well taken care of, just for some really odd reason she seems to excrete a lot of oil?

Does anyone else experience this issue? Any advice you can give? Thanks!