Place the cookie sheet outdoors on a flat surface.
Pour vinegar onto the cookie sheet until the entire surface is coated. Leave the sheet outside to soak overnight, then pour off any remaining vinegar.
Scrub and rinse the cookie sheet in hot water. If the burnt sugar remains, continue scrubbing.
Pour hydrogen peroxide onto the cookie sheet, and bake it 30 minutes in an oven preheated to 350 degrees Fahrenheit. The boiling action of the hydrogen peroxide works to dissolve the burnt sugar.
Remove the cookie sheet from the oven with hot mitts.
Pour the remaining peroxide down the drain, and let the cookie sheet cool until it is safe to handle. Scrub the cookie sheet with scouring pads. Repeat as necessary until the cookie sheet is clean.