Remove the feta cheese and any other foods in the surrounding area from the refrigerator. If the smell is very strong, empty the entire refrigerator for a thorough cleaning. Place the feta cheese in an airtight container to keep the smell from permeating into the refrigerator again.
Fill a bucket with 1 gallon hot water. Add 1 cup baking soda and 1 cup white vinegar to the hot water.
Clean the inside of the refrigerator, especially at the source of the smell, with the baking soda and vinegar solution to remove cheese residue and odor. Both vinegar and baking soda are effective, natural cleaners and deodorizers.
Wipe the inside of the refrigerator with a damp cloth to remove baking soda residue. Dry with a clean cloth. Prop the refrigerator door open and allow it to air dry for 10 to 15 minutes.
Cover the bottom of a shallow baking pan with fresh coffee grounds. Place all the items back in the refrigerator then put the coffee grounds in the refrigerator. Allow the coffee grounds to remain overnight to absorb any remaining feta cheese smell.