Appliance Repair Questions? Ask a Technician for Answers ASAP
It is possible you could be finding grease from the bearings working its way into the drum, though not very common.
Start by inspecting the drum with a torch to see if you can see any sines where the grease is coming from, if you can see signs inside the drum it a case of stripping the unit down and seeing if the bearings need replaced or just cleaned up with a rag.
If you cant see anything in or around the drum, then its very unlikely the marks are coming from the dryer.