Unscrew and remove the screen from the vent hood. Look up into the vent and inspect the first duct flap. If it is stuck open, nudge it to close it. Flaps usually stick open due to a buildup of grease. Clean the inside of the vent with the degreaser and nonabrasive sponge.
Inspect the external vent cap and its internal flap on the outside of your house. This may be on a wall or on the roof. If the flap is stuck open, close it. Clean any debris that may be causing it to stick. If the external cap does not have a flap, or it is of low quality or in disrepair, replace it with a high-quality vent cap. Some of the most effective caps have felt-lined edges to improve the air-seal.
Make sure the vent cap is properly sealed where it meets the wall or roof. Apply new caulk to the joint if there is no caulk or if the current caulking is damaged.
Insulate any portions of the vent duct that run through the attic or other unheated areas. Use spray-foam or other approved duct insulation. Warm air from the kitchen naturally rises to fill the duct when the fan is not in use. Insulating the duct helps keep this air warmer, slowing the cooling effect that ultimately leads to cool air dropping down into the kitchen. Insulation also minimizes condensation inside the duct.
Make sure that all duct joints are properly sealed with foil duct tape approved for use on ductwork. Remove any old tape, if necessary, and wrap all joints with the new tape to create a complete air seal. Do not use standard plastic-and-cloth duct tape, as it quickly deteriorates and fails to seal joints.