The rear trigger guard screw doesn't really mount the action, it only secures the trigger guard to the stock, so it should not be a problem.
To remove the action from the stock, you shouldn't even touch the trigger guard screw.

If I remember correctly from adjusting trigger pulls on just about all of my Savages - both model 10s and 12s - the action mounting screws are different lengths.
It is possible that someone mixed up the mounting screws from two different Savages and put two short screws in your F-Class.