Sorry, you can't clear the screen: when you catch the red guy, it's not removed but its position is randomized instead. Don't ask me why I took this approach, I suppose it made sense at that moment.
Tip: you can move faster than the red guy when moving in diagonal due to 8-way movement not being perfect. They all move in a straight line but take a new random heading after a random distance or at screen bounds. So there's no real AI. I was amazed to see that a similar logic worked so well in another entry.