A trick that worked for the Otterbox on my wife's Galaxy S3 might work here as well:
First clean the display and the inside of the screen protector. Get some baby powder and while leaving the top closed shake up the container to get the powder into a fine dust inside. Take the screen protector and hold it above the shaken baby powder bottle(?), open the top of the powder and squeeze the bottle so a powder cloud comes out and slightly dusts the inside of the screen protector.
Put the case back together and hopefully the oily film is gone. Clean/Repeat as necessary.
There are videos on YouTube showing this solution. Some use the powder on the device, I think it's wiser to do it on the case/screen protector.
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Last edited by An Droid; 14th January 2015 at 08:25 PM.