if it's gone on to wood you've had it. the dye will have penetrated the grain the only way to get it off is to sand it down.I know it happened to me on my bathroom cabinet.i sandede it down and re varnished it it looks ok !! Good Luck!
That's why I gave up dying my own hair and now go to the hairdressers, it doesn't cost me anymore really as I ruined towels, a dressing gown, had to repaint the radiator etc!!!!!