The grade of “C” is often seen as a middling grade, earned by someone who gets by but does not excel. The term “gentleman’s mark” for the grade “C” has been cited in print since at least February 1905.  “C is a gentleman’s grade” and “the gentleman’s C” have both been cited in print since at least April 1906. All of the early citations are from Harvard University.
 
“Gentleman’s C” is still commonly used, with “gentleman’s mark” and “gentleman’s grade” both infrequently used.
 
 
(Oxford English Dictionary)
gentleman’s C n. (also gentlemen’s C) U.S. an academic grade of C, as said to be (undeservedly) awarded to a student of high social status and low academic ambitions.
[1907 Educ. Rev. Apr. 386   The saying that ‘C is a gentleman’s grade’ is evidently an imperfect defense for the idler in Harvard College.]
1922 C. Britten in H. E. Stearns Civilization in U.S. 127   He crams through a few febrile nights of cloistral deprivations and flagellations; and the sun shines again on his harvest of gentlemen’s C’s.
1952 L. W. Ferguson Personality Measurem. xv. 400   A person who decides that he is going ‘to make’ Phi Beta Kappa has a higher level of aspiration that the student who decides he is going to be satisfied with a gentleman’s C average.
 
Google Books
February 1905, Metropolitan Magazine, “The Spiritual Quality” by E. S. Martin, pg. 538:
There are five grades of scholarship at Harvard. The middle grade is “C.” Dr. Eliot quoted a remark that he had heard, that the gentleman’s mark was “c.”
(...)
The best that can be said for the foolish notion that “C” is “the gentleman’s mark” is that “C” is a better mark than “D,” and at least implies that the young gentleman is paying enough attention to his scholastic duties to maintain his connection with the college.
 
Google Books
April 1906, Harvard Illustrated Magazine, “Shall Quality Count for the Bachelor’s Degree?” by William Trufant Foster, pg. 148:
The scholars of the first group at Harvard could give learned reasons, no doubt, to show the absurdity of the common saying that “C is a gentleman’s grade.”
Pg. 151:
Under any plan formulated on this general principle of counting both quality and quantity for the degree, the student who is wandering leisurely in Commonplace Lane, well content with a mere pass-mark, can no longer tell you that “the gentleman’s C” is as good as any other grade.
 
Google Books
April 1907, Educational Review,  “The Gentleman’s Grade” by William Trufant Foster (Bowdoin College, Brunswick, ME), pg. 386:
“The saying that ‘C is a gentleman’s grade’ is evidently an imperfect defense for the idler in Harvard College.”  So says the report of the President.  (...)  The grade C stands for Commonplace Lane, no doubt: and, by a kind of majority vote, it stands for “the gentleman’s grade.” All students like to be considered gentlemen, and a majority would attain no such distinction if the demands of scholarship were higher. Indeed the C men would win every time on a (Pg. 387—ed.) two-thirds vote. President Eliot, in praising what has been done at Harvard to raise the standard of daily workamong the less ambitious students, taken alphabetically from the class of 1905, only 36 attained A or B in even half their courses.
 
Google Books
Civilization in the United States:
An inquiry by thirty Americans
By Harold Stearns
New York, NY: Harcourt, Brace and Company
1922
Pg. 127:
... and the sun shines again on his harvest of gentlemen’s C‘s. the proud though superfluous A or B, abd maybe a D that bespeaks better armour against the next onset.
 
At War with Academic Traditions in America
By A. Lawrence Lowell
Cambridge, MA: Harvard University Press
1934
Pg. 349 (from Annual Report, 1931-1932): 
“C is the gentleman’s mark” is no longer a phrase to express a belief, or excuse indolence.
 
What a University President Has Learned
By A. Lawrence Lowell
New York, NY: The Macmillan Company
1938
Pg. 69:
This was the time when “C was the gentleman’s mark”; when, in fashionable groups, outsiders of scholarly rank were as a class often referred to as “greasy grinds”; when “prizes should be left to greasers.”
 
24 May 1938, Greensboro (NC) Record, “Tea Time Topics” by Nell Craig, pg. 5, col. 1:
Good-bye to the gentlemen’s C degree and to any college red tape which established it as desirable, and welcome to any requirements for admission to college or work there which hurry on maturity and a civilized point of view.