Green’s Dictionary of Slang

(US) annoyed, irritated, upset.

1941		C.R. Bond 5 Jan. in A Flying Tiger’s Diary (1984) 45: The Old Man was still teed off about Ricketts’s landing yesterday.
1951		M. Spillane One Lonely Night 48: You’re teed off because you were done out of a kill.
1958		E. Dundy Dud Avocado (1960) 42: There’s only one reason you were so teed off with me when you found out that I was a virgin.
1958		E. Gilbert Vice Trap 11: You still teed with me about Lona, man?
1965		F. Pollini Glover 18: He got teed off.
1969		C. Sellers Where Have All the Soldiers Gone 13: His tentmate was gone into the village, teed off because Lee hadn’t ‘lost’ any morphine on patrol.
1970		B. Seale Seize the Time 59: Man, they were kind of teed off.
1975		L. Rosten Dear ‘Herm’ 54: Well, I could just spit I am so T’d off!
1989		H. Rawson Dict. of Invective (1991) 385: More commonly encountered today in such phrases as tight as a tick (very drunk), lively as a tick in a tar-pot (motionless), and tick(ed) off (angry). The last one [...] is a variant of tee’d off, in turn a euphemism for pissed off.
1997		T. Winton Lockie Leonard, Legend (1998) 79: Lockie’s getting teed off.