Allow the stove top and burnt polyester towel to cool completely.
Dampen a clean cloth with water. Wring out excess moisture. Heat the cloth in the microwave for 30 seconds on the "High" heat setting.
Remove the hot, moist cloth from the microwave with tongs. Lay the cloth directly over the burnt-on towel stain. Leave the cloth in place for five to 10 minutes to soften the melted towel.
Lift the cloth off the smooth stove top surface. Gently scrape the softened towel residue with a scraper made for glass. Remove as much of the burnt-on towel as possible.
Wet a clean cloth with nail polish remover. Wipe the remaining burnt towel residue with the nail polish remover to dissolve the stain. Rinse the surface with a damp cloth.
Place two drops of dish washing detergent on a damp cloth. Clean the surface of your smooth stove top with the detergent. Wipe the stove top with a damp cloth to rinse it. Dry the surface with another cloth.