The red "3ivx" appears on your computer for reasons that have nothing to do with Snow Leopard or Mountain Lion.
They appear because at some point in the past, you downloaded the free 3ivx software from
www.3ivx.com in order to play movies. The free version is limited; you can play moves for a certain amount of time, and then it puts the red "3ivx" logo into the movies until you pay for the unlocked version.
You don't need to upgrade your computer's operating system. You need to remove 3ivx and use a different movie CODEC package, like DivX for Mac.
