Combine 1 cup white vinegar, 1 cup rubbing alcohol, 2 cups warm water and 10 drops dish soap in a spray bottle. Also add in either 1/4 cup mineral oil or baby oil.
Moisten a paper towel with solution and place over the plastic residue. Let the paper towel sit in place for 20 minutes or so. Rub over the area and most, if not all of the plastic residue, will wipe away easily.
Wipe the stainless steel surface with a clean, dry paper towel. This solution not only removes plastic residue but also works well as an all-purpose stainless steel cleaner.