I had a pen explode in my clothes dryer! In addition to ruining a couple of perfectly good shirts, there is now ink on the inside drum. It’s dried ink, but I’m not sure I can trust it to dry my next load of laundry.
What will take this ink off the drum? Thanks for your help!
I assume it was a ball point pen. Right?
You might try laundry detergent with a little water, it just might do the job.
Try mineral solvent, paint thinner, or similar product next. If that fails it may require a solvent type paint remover. It may be necessary to remove the drum for a cleaning of the outside if any was transported through the holes.
I think the answer is going to depend on the type of ink? Is it water or oil based?
Chlorine bleach will remove most types of ink, except for ball-point pen ink, which has an oil base.
It was a cheap ball-point.
I’d start with Goof-Off which works really well, but isn’t too nasty, as solvents go. Next up on my list would be VM&P Naptha, aka charcoal lighter fluid. Beyond that would be acetone, and I don’t recommend you go further, as normal citizens shouldn’t be messing with some of the other solvents I have in the shop. 
Safety notes: use any of these products in a well ventilated area-set up electric fan or fans to move flammable fumes out of the area and not deprive you of good breathing air. Extinguish all pilot lights in the area, do not smoke, and don’t start/stop electrical equipment owing to the possibility of an arc. Properly dispose of all rags/paper towels used to clean the dryer, and place them outside the dwelling.
I just went through this, too.
I did a quick search, and the recommendations were things like paint thinner, nail polish remover, things like that.
I tried these on the marks (separately), and none of it helped. I’ve been using the dryer since, even on white things, and none of the ink has come off on anything.
So if you find you can’t get the ink off, the likelihood is that it will be safe for your wash, too.
Note that they recommend you try the removers in a well-ventilated area, and make sure it is thoroughly dry and the removers cleaned out before trying to run the dryer.
I’ve had good luck with WD-40 getting stuff like crayon and grease off things.
I have pen marks in my dryer, too, and they don’t come off on the clothes. Try running a junky towel through there first to see it the ink is set.
After cleaning away any immediately visible traces (by the methods recommended above, but if you’re using anything solvent-based, be really sure that it’s all evaporated before you start the machine up again, otherwise you might have to deal with a kaboom), I’d sacrifice a very large old towel (or several) - wet with water and a little detergent, wring out and put through a drying cycle.
After a certain amount of solventing, you gotta figure if you can’t get it off, neither can the dryer and you’re set.