First of all I doubt your monitor was calibrated properly which is the root of the problems you are seeing.
Not only does blue check need to be done but the gain and bias adjustments need to be done to verify the monitor is actually producing white and black properly.
Do you have a waveform monitor available and a dsc chart to confirm if your camera actual does have a green color bias.
Without first confirm which piece of the chain has the problem it is impossible to determine what is causing the problem or if it is indeed a misaligned Varicam. The problems could range from preset gains being off, white shading lens alignment, monitor gain and bias adjustments etc etc.
Does the facility or owner you rented the Varicam from have the necessary test gear (ie waveform, DSC chart, camera black out room lab) to setup a proper baseline reference for the camera. Until this is done all bets are off.
Listen to Leo and myself and hire yourself a properly qualified video engineer to set up the camera and or monitor so you are not chasing your tail out in the field.
The money will be well spent instead of wasting additional money in post to color correct errors caused by misaligned field equipment or operator error.
Tony Salgado