The correct answer is C) periodically removed for inspection and lubricated. The pivot pin at the base of a sheath-screw boom davit must be periodically removed for inspection and lubrication to ensure the proper functioning and safety of the davit system. This is a requirement under the regulations governing the maintenance and inspection of Coast Guard-approved equipment. Regularly inspecting and lubricating the pivot pin helps prevent wear, corrosion, and potential failure, which could jeopardize the safe operation of the davit and the associated boat or liferaft. The other options are incorrect because: A) replacing the pivot pin at each inspection is not necessary, as long as it is properly maintained; B) the locked position of the pivot pin is important, but this does not address the need for periodic inspection and lubrication; and D) the pivot pin should not need to be inserted each time before the booms are cranked out, as it should be in place and properly maintained at all times.