Steven Gillman explains how you can use your hair dryer to remove gum from your carpet:

“Just heat the gum, being careful not to melt any carpet fibers. Then you can use a piece of plastic wrap or a plastic bag to lift the softened gum away. Allow it to stick to the plastic, and pull it up. This will often get most of the gum.

For the remaining chewing gum, apply Extra Strength Ben Gay, or another muscle rub containing methly salicylate. Use plastic or a rag to pull more gum out, repeating the process if necessary. Once you completely remove the chewing gum from the carpet, clean the spot with a mild detergent solution (a few drops of dishsoap in a cup of warm water). Rinse the area with warm water and dry quickly, first by blotting up any water, then with a fan, if you have one.”