What do I replace if the inside of my iPod nano 6g screen is dirty?

I accidentally spilled some oil on my iPod's screen. It was not a lot and it did not get inside the USB nor the headphone jack. I immediately tried it afterwards and it functioned normally, except there's an oil stain in the interior of the screen.

So I followed a video to open up the device and I took apart the different layers of the screen to wipe each of them clean. However, the oil won't come off for some of the plastic layers behind the LCD screen.

Does anyone know what part I should replace? I'm not sure what the Touch Digitalizer is and I didn't see it inside either so I'm not sure if that's a problem. I know that my LCD screen is not broken, it's functioning properly. The glass part is good. It's just the plastic layer at the bottom of the screen (the last part of the screen) that is having a problem. Thanks in advance!