Measure the gap between the top of the metal door sill and the bottom of the door. Purchase a piece of plywood that is as thick as this measurement. Cut the plywood so it will fit between the door frame and be hidden beneath the metal sill.
Remove the screws holding the metal door sill in place. Pull the door sill off of the threshold and out of the door opening. Gently hammer the sill out from underneath the door frame if it is installed beneath it.
Lay the piece of plywood on the door's threshold. Secure it in place with screws. Set the metal door sill on top of the plywood and check how it fits in the door opening. Cut the sill with a hacksaw so that it fits between the door frame if it was previously installed below the door frame. Set the door sill aside.
Spread a few beads of silicone caulk along the surface of the plywood. Position the metal sill onto the plywood and secure it in place with screws. Close the door to check that it does not rub against the sill and that the gap is gone.