I'm always a little puzzled when people's first assumption when there's anything they don't understand is that their phone has been taken over by someone competent enough to do it but incompetent enough to make it really obvious that they are doing it. That usually seems a little unlikely to me: I worry more about the app that's silently stealing data myself.
Can you give a detailed and precise description of what you are seeing. Phrases such as "the shady looking green guy" might be amusing but they are also completely unclear (unless the Hulk has hacked your phone, which isn't his style, the only "green guy" I can think of is the android logo, but I've never heard that called "shady-looking" before). Context helps: what you are doing, what else is on the screen at the same time, where he appears, what is on the screen when it wakes, etc.