"I advise you to call a halt to this feud before somebody gets hurt. In the meantime, contact the Office for the Removal of Curses, Jinxes and Hexes, who will take care of both the broomstick and your brother."
An office in the Ministry of Magic, specialising in stopping and removing non-injury causing magic spells
The Office for the Removal of Curses, Jinxes and Hexes is not specifically assigned to a department within Ministry headquarters, but Dempster Wiggleswade of the Department of Magical Law Enforcement answers an enquiry in the Daily Prophet which implies that they will take care of both removing a jinx from an object and dealing with the family member who hexed it in the first place. (DP3)
While the date printed on DP3 is 1 June 1999, the timeframe for these events is 1992-1993.