I have seen smears such as you are describing coming from the pressure roller that feeds the paper through the printer. Try opening the lid of the powered down printer and look inside with a flashlight to see if you can tell where the smear is on the mechanism. With luck the original smear that is getting transferred to the back of your page will be visible and relatively easily reached and you can clean it up with something like an alcohol swab.

If the smear recurs it would probably be cheaper to replace the printer than it would be to repair. Manufacturers make their money from the ink and sell the printers at close to break even.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein