Before you go so far as to remove the screen, try this handy trick I just found on YouTube (link below):
1. Turn off the iPad.
2. Place the iPad face down on a hard surface with something on it to keep from scratching the screen.
3. Knock on the back of the iPad.
That's it! I just used that to fix a screen that was even crazier than yours.
https://www.youtube.com/watch?v=ayRPWsvZvAA