This question is wholly seeking historical evidence and not about physics. It is a follow on from the Physics Stack Exchange question:
The answer is a definitive yes. A simple back of the envelope calculation with the Schwarzschild metric shows that the order of magnitude deviation between corresponding points Earth-Moon transfer trajectories calculated with Newtonian and GTR physics is of the order of 0.1 meters (you read that right- the length of your tallman finger). A neat approach to the problem is John Rennie's answer here.
This conclusion MUST have been reached by NASA (or even NACA) in the leadup to the Apollo landings. I should like to know any of the following how was the conclusion reached, who first raised the question and when. A link to / citation of a report would be great. I suspect the question arose and was resolved in one of three ways:
The general relativity / gravitation literature holds this calculation done in the first half of the 1900s in the early days of "dreaming" about reaching the Moon (although I can't seem to find anything), and the relevant papers were known to orbital mechanical scientists;
The question was raised very early in the NASA programs, and quickly resolved by a back of the envelope calculation like John's. If so, I'd expect that there would be somewhere in the archives a short report of one or two pages comprising a calculation like John Rennie's with the endorsement of a prominent GR theorist of the day, like John Wheeler. This would be dated 1950s / early 1960s;
Empirically. Once Mariner / Ranger data became available, there would be no noticeable error between Newtonian theory and observations, so the question was never raised. GTR effects would be utterly swamped by others. In particular, I learnt today that the error Frank Borman was referring to when he said that Apollo 8's final position error after lunar orbit insertion was "about a mile and a half from where we were supposed to be" was indeed owing to five high density "lumps" on the Moon's surface see "Bizzare Lunar Orbits" here (Thanks to user David Hammen for this knowledge) and that the calculation error was thereafter reduced to a 120 meter difference between calculated and actual landing position for Apollo 12. Still three orders of magnitude bigger than the GTR effects.
So, in summary, references / answers to whom the question was raise by, when and how was it answered?