"They left half of themselves behind. So, of course, they were stuck. Couldn't move either way. Had to wait for the Accidental Magic Reversal Squad to sort them out."
-- Arthur Weasley about splinching (GF6)
The Accidental Magic Reversal Squad is a division of the Department of Magical Accidents and Catastrophes at the Ministry of Magic. This team is the first on the scene when a magical accident or catastrophe occurs.
The Accidental Magic Reversal Squad is responsible for reversing the effects of accidental magic, or spells that have gone wrong, especially those produced by inexperienced witches and wizards. The team includes trained Obliviators to modify memories of Muggles on the scene.
Two members of this squad were responsible for dealing with the effects of Harry Potter inadvertently blowing up Aunt Marge (PA3) and modifying her memory (Pm). They also deal with the after effects of splinching (GF6) and were called out to deal with Goblin riots in Chipping Clodbury (DP3).
It is referred to as the "Accidental Magic Reversal Department" in earlier editions of the books (PA3).
While the date printed on DP3 is 1 June 1999, the timeframe for these events is 1992-1993.