Nah, don't think you need to remove the gripframe to clean the eyes. Well I never have anyway, don't know why you'd need to???
First off - don't blame me if you screw your eyes up!
Now, onto the business at hand...
Most important thing here is DO NOT PULL THE WIRES TOO HARD.
So, take the cover plates off and then pull out the rubber detents and springs (don't lose them!)
Use a small and blunt nail to push through the opposite side hole (where you have removed the detent from) and into the eye you want to remove. They are quite hardy and they do need a bit of a push. Once one eye is removed the other one is easier as you can use the hole directly opposite (where you have just removed the first eye from) to put your nail through.
Just make sure whatever you use to push on the eyes is a. stiff enough (paper clip will just bend) and b. blunt enough (otherwise you may damage the eye). I used a nail and it worked fine
Finally, on reassembly make sure that you push the eyes in fully, otherwise they will not align and you may get stuttering strings (as it can't read the balls correctly). Basically make sure you try it again after performing the above procedure before using it for a tournament or similar.
As a final note I would say do the eye removal thing as a final measure. If you can get a cotton bud or similar in there to clean the eyes do that first as it's always a little risky. Good luck...