If Ken's method does not work, though I suspect it will work very well............I have used mineral spirits dabbed on and allowed to dry on grease stained antiques and other woodworkers have warmed grease spots with a hair dryer and allowed fullers earth also warmed to sit on the spot overnight and absorb the oil residue.
Removing grease spot
You might try ironing out any remaining cheesiness... put down a soft cloth or even a double layer of paper towel. Place it over the spot and iron on medium heat. that should make any grease rise into the cloth or paper towel. After that, then tung oil should be the perfect finish. I finish almost all my instruments with tung oil; I like the satin finish you get after about 4 coats.
Um... that will actually become rancid. I would suggest not.