According to Good Housekeeping Magazine, the first step in removing melted gum from a dryer is to heat up the gum by placing old towels into the dryer and running it on warm for 1 to 2 minutes. The next step is to create a paste using 1 tablespoon of laundry detergent and water. The last step is to apply the mixture to a washcloth and scrub inside the dryer.
To ensure all traces of gum are removed, first run a full dry cycle of old, wet rags prior to drying a fresh load of laundry. Checking all pockets and hidden compartments on garments prior to washing and drying helps to prevent repeat occurrences.
If gum has melted onto clothing during a drying cycle, it can easily be removed by placing the garments into freezer-safe bags and placing the bags in the freezer overnight. After the gum has hardened, scrape it off of the garment with a dull knife. Pre-treat any remaining stains with dish-washing liquid and distilled white vinegar, and wash the garment on a regular cycle. If the gum is firmly embedded, it can be loosened with a small amount of petroleum jelly. Once the gum has loosened and is removed from the fabric, pre-treat the oil stain with cornstarch and a solvent-based laundry spray prior to washing.