Green’s Dictionary of Slang

(US campus) a note sent to a student warning them to work hard and generally ‘get a grip’.

1921		DN V 111: CA [Students’ terms], Cinch, cinch-notice [...] A warning sent by the college authorities with the object of tightening the student’s hold on his work.
1968		M.A. Watkins ‘Some Notes on Flunk Notes’ in AS XLIII:1 76: Some colleges in California and Nevada, also borrowing from cowboy lore (or, less poetically, from the stable), use terms like cinch notice and cinch to refer to their deficiency reports ... The idea of squeezing or being squeezed is, obviously, inherent in the meaning of the terms.