Green’s Dictionary of Slang

to place at a disadvantage.

1865		Sydney Morn. Herald 31 Dec. 8/6: [from Macmillan’s mag, London] One is said to ‘score off’ or ‘notch’ any person over whom one obtains any advantage either in word or deed.
1870		Argus (Melbourne) 15 Jan. 1/5: One is said to ‘score off,’ or ‘notch,’ any person over whom one obtains any advantage eithor in word or deed.