This is how the word pronounced tit (and often spelled that way) is actually spelled. Due to the slang usage of this word and the fact it refers to the breast (making it a naughty word), the mispelling is all too common.

Teat (?), n. [OE. tete, titte, AS. tit, titt; akin to LG. & OD. titte, D. tet, G. zitze: cf. F. tette, probably of Teutonic origin.]

1.

The protuberance through which milk is drawn from the udder or breast of a mammal; a nipple; a pap; a mammilla; a dug; a tit.

2. Mach.

A small protuberance or nozzle resembling the teat of an animal.

 

© Webster 1913.