Green’s Dictionary of Slang

(US) something that provokes laughter.

1922		Wash. Times (DC) 16 May 16/4: We were prepared for a big tee-hee. Instead of a laugh [...] we received a distinct shock.
1976		Dly Jrnl (Franklin, IN) 16 Nov. 2/3: A Carter presidency clearly is not going to be a riot of giggles [...] Not, mind you, that it should be one big tee-hee.

(US) to laugh at.

1907		D. Runyon ‘The Defence of Strikerville’ in From First To Last (1954) 12: We didn’t want the gang [...] to give us the big tee-hee.
1919		Eve. Star (Wash., DC) pt 3 16 Nov. 3/2-3: A young ‘fluff,’ applying for ‘bale’ [...] was given the big tee-hee ’cause she couldn’t prove her age.

reduced to laughter.

1902

Richmond Dispatch (VA) 12 Oct. 13/2: I guess he got sore but I had everybody else on the tee-hee.