Assuming the screw exists, in my opinion, it's purpose is not to make the lock easier to fire. It is there so that the nose of the sear won't be deeper in the full **** notch than it needs to be.
How much engagement does it need to have? Again, in my opinion, the full thickness of the nose of the sear should be engaging the full **** notch with the corner that is the first to disengage with the notch right at the outer edge of the notch.
Yes, there are people who screw the adjustment screw in so that only half or less of the thickness of the sear nose is engaged with the notch. Some have even gone so far as to adjust it so that only a few thousandths of an inch are engaged, but by doing this they are making the gun dangerous to use and they are increasing the possibility of the nose of the sear breaking off.
As we know, if the sear is almost ready to let go of the full **** notch, a slight bump on the stock can cause it to release causing the gun to fire.
If the material of the sear breaks because too small of an area of the sear is trying to keep the gun at full ****, the gun can fire even without the stock being bumped.
It's a good idea to use this adjustment screw to set the nose of the sear for a 100 percent engagement. If it is deeper than that then yes, by all means screw the screw in to reduce it but if the sear is engaged less than the thickness of the nose of the sear then by all means, unscrew that screw to increase the sear's engagement.