The answer is neither Technician is correct (Answer C).
A standard spin-on oil filter has a rubber seal built into it, and no gasket is required to assist in forming the seal. Also the engine mount has nothing to do with the question as if there was a gasket (which there is not), it could get stuck to anything or fall on the ground during removal of the related parts.
The second technician removing the oil drain plug on the sump is also incorrect using a screw driver. Almost universally, oil drain plugs are threaded bolts and require a socket (not screwdriver) to loosen and remove. This is because they are under a tension (torque value) far above what you can generate by hand with a screwdriver.
