There could be several causes of your problem, but top of my list would be:-
- The driver circuit to the green gun.
- The Tube
The only way to be sure is for someone with technical knowledge to monitor with a scope the three colour signals into the tube with a constant test signal the same on RGB, if the result is equal signal at the tube, then the tube is at fault. If the green signal is higher, then the problem is going to be in the driver circuit.
Frankly, unless you are an electronics or TV engineer, you will need to get your dealer to look at it.