What is the oily film under the screen lens?

I purchased a used new 3DS xl and replaced the scratched screen cover and made the mistake of cleaning the screen under it (to remove the dust) and doing so I ended up smearing around this oily film that I had to remove completely after making streaks. I think it is some anti reflective film or some sort of anti glare. Can I re-add it or do I need a new screen. The 3D affect is slightly off now.