The "white paper" is just the cover for the backlight so it does not get scratched during shipment. If you see a little tab hanging off, you can be sure this is what it is. It should be removed before installing the screen, as it's presence can cause the screen to not fit, or the LCD may break.
Since your LCD still worked, I dont think you have much to worry about, just carefully remove it. Check your digitizer connection. Its a weak and annoying connection that can be difficult sometimes. Ensure you rememebr to tape it back up with the copper tape!
The biggest thing to remember is to maintain your cool. If you start getting rushed and agitated it is VERY easy to tear the volume/power ribbon while installing the digitizer connection. Unless you have tiny fingers, use a nylon tweezers to set the connection. Unscrewing the front camera nearest the digitizer connection also gives you more room to work without damaging anything. Good luck!