Take the door off!
Just watched the first season episode where the x is painted on the door of the house.
It ended with Ben and his wife ineffectually rubbing at it with watery scrubbing brushes.
Is he a handy man? Is she a savvy woman?
As soon as is convenient, remove the door from the frame with a screwdriver, take it into the garage or the backyard, put it on some trestles or a bench and work on it with turpentine and/or a scraper at your leisure. If it's not getting results, replace the door or just go without it!
This really annoyed me for some reason.