Cover greasy smudge marks with cornstarch. Allow the cornstarch to sit on the stove top surface for five to 10 minutes to absorb the grease.
Dampen a paper towel with warm water. Wipe the cornstarch off the stove top with the paper towel until removed.
Fill a spray bottle with 1/2 cup water and 1/2 cup white vinegar. Spritz the remaining smudge marks with the diluted vinegar solution until dampened.
Cover a damp sponge with baking soda for a safe, mild abrasive to remove stubborn smudge mark stains without scratching the surface.
Remove any remaining smudge marks by scrubbing the marks with the vinegar and baking soda.
Rinse the stove top surface by wiping it off with a damp paper towel. Dry the surface with another paper towel.