Sven,
This is a nice find showing the holes as designed and built by Perry Maxwell. The club's original course was elsewhere in the city and was redesigned by Tilly in 1920-21. One hole in particular stands out to me, the par-3 third hole. The caption describes it as the "remodeled par-3 third." This appears to confirm that the changes Tilly recommended to the club on January 14th, 1936, the day he stopped at the club as part of his PGA course consultation tour. That night, in his letter to the PGA, he wrote: "This morning I visited the course of the Oklahoma City Golf and Country Club. With [P.G.A. member Francis] Scheider I went over every hole of this fine course. As a matter of fact there was so little to criticize, as he asked me to do freely, that I was only able to help him in one instance. This involved the Third green (149 yards), which was wrongly contoured and with much wasted space. Almost in the center of the green was a prominent hummocky undulation, which obviously introduced a large element of luck, particularly in view of the fact that this green is reached properly with a lofted iron, which might end anywhere, depending entirely upon the particular slope of the undulation it might strike upon. Conferring over this with both Scheider and Frank Bristow (Governor of the Club) [both] entirely agreed with me and it will be corrected."
Further corroborating this, Bob Burkes' 2012 history of the club states: "In late 1935, directors of the club asked renowned golf course architect A. W. 'Tilly' Tillinghast to visit the course and make recommendations for improvement...Calling it a 'truly fine course,' he found fault only with the third green. Club officials agreed with Tillinghast's findings and gave instructions to remedy the problems."