"even though you don't use a screwdriver to disassemble the Mauser..

-Occams razor says the "screwdriver" is an Allen/ Hex key in screwdriver form.

...(although you might use it to adjust the scope but then you also need to fire rounds to test the adjustments which he clearly wasn't doing)."

Likewise Occam proposes the scope itself wasn't dismantled then reassembled on the roof: it would have been left attached to the gun body which was merely unscrewed from the stock.