Yes they do leave a residue. Dryer sheets are nothing but a very fine coat of oil. This eliminates static cling. I never wash my car towels in the washer with fabric softener or dryer with dryer sheets.
Best way to remove the coat of oil in your dryer is to run some wet towels through it. It only takes a few wet towels to clean it up.
Then, in the future never use more than one dryer towel per load of laundry when washing your clothes. That is why they tell you to use only one sheet.
I found out the hard way. My wife used to use 4-5 dryer sheets in our dryer for our clothes. My car wash towels never seemed to soak up water very well. Finally figured out why. They were coated in the same oil the dryer sheets are coated in.