Jim Hoak is correct, the Finkbine that exists today was built around 1953. The old course was on the other side of the Interurban RR tracks, stretching from Highway 6 in Coralville (where the soccer fields along the Coralville strip are now located) up to the area where Kinnick Stadium and the Children's Hospital (which some of you will know from "The Wave") are located. That's why there's a Golfview Ave in University Heights directly across the tracks from Kinnick, something I had always wondered about previously.
Never seen a scorecard for the full 18 holes before, that's a nice find! When I first started playing there were 4 or 5 holes remaining of the original course along the Coralville Strip, which was referred to as "lower Finkbine". They were mowed but not otherwise maintained and with free access. Good place to hack it around as a 10 year old to learn the game. I remember there was a bad drought that year, not only was the "course" uniformly brown there were huge cracks in the sod even in the "greens". I remember losing my ball down one at least once!
I had been under the impression the "upper" holes were removed when Kinnick Stadium was built in 1930, and it had become a nine hole course. Obviously that was not the case, based on that 1950 scorecard reproduced above, so there must have been some re-routing done. At any rate once the new Finkbine was built I'm pretty sure the upper half was abandoned, and sometime between then when I first visited there in the mid 70s several of the lower holes had been abandoned and become overgrown due to repeated flooding. The soccer fields were built sometime in the early/mid 80s I believe, removing the last vestiges of the original Finkbine.
One thing of note - I have no idea how the routing worked and where the 1st and 18th holes were located. Given the distance involved I'm not completely convinced it was an out and back routing, but might have been more like Dismal's Red where you start in one place and end in another. The distance between two points where I know part of the course existed is about 1.25 miles, and the layout I know about from the lower part doesn't leave much room for an out and back. I know that's by far more likely, but I have trouble seeing how it worked based on what I know, its length shown on the card, and the fact you wouldn't have had long green to tee walks in a course designed over a century ago.