There are several suggestions for removing ink from your dryer provided by LoveToKnow. Most of the tips use items you may already have in your home.
The first step in deciding how to remove ink from your dryer is determining whether the ink is on the drum or the paddles. The drum is typically made of steel or porcelain, while the paddles are made of plastic.
If the ink is on the drum, the simplest solution is running the dryer on high heat, which will bake off the ink and allow you to wipe it away. Another option is wiping it off with nail polish remover while the drum is warm. WD-40 or vegetable shortening placed directly on the stain may also allow you to wipe it away. You can also soak a towel in bleach water, wring it out and run it in the dryer for a half hour.
If the ink is on the paddles, it may be harder to remove, especially once the dryer heat sets the stain. You may be able to scrub it off with Mr. Clean Magic Eraser and warm water. Rubbing alcohol on cotton is another option. Otherwise, you might be able to remove the ink using bug spray, which will sometimes lift out the ink when sprayed directly on a stain.