How to remove plastic covering on guitar pickguard?

I bought my American Strat about 3 months ago, and I've yet to remove the plastic covering on the pickguard. Lately, it's become very grimy looking and some markings have shown up. I really want to remove the covering, but peeling off the sides don't help me at all! I can't grasp and it's really stuck! How do I remove it, I've taken out a few screws in the pickguard, but I still can't get it! Help me please!