NY Times investigative reporter Phillip Shenon wrote a book a few years ago on the Warren Commission investigation ("A Cruel and Shocking Act") and used the Thomas controversy for part of it. He interviewed the surviving family members and others and, based in part on those interviews, argued that the US government failed to adequately check out Oswald's alleged activities when he went to Mexico City.
Thomas and then US Ambassador to Mexico Thomas Mann both believed that based on Oswald's activities in Mexico City that there may have been either Soviet or, more likely, Cuban involvement in the assassination. This was based mostly on the so-called "Twist" party (yes, the Chubby Checker's dance "twist") that Oswald allegedly went to when he was in Mexico City. The allegation is that he met several Cuban officials - including Cuban intelligence figures - at this party. It was here, supposedly (somehow), that he coordinated his future attempt on JFK with Cuban agents. He was, again somehow, instructed on what to do and how to escape.
All of this occurring, of course, about two months before the assassination and well before Oswald had the job at the TSBD or even before JFK agreed to visit Dallas. It makes almost no sense to me on any level (he's meeting Cuban intelligence officials at a party? why not privately?).
According to Shenon's account, both Thomas, who worked for the State Department in Mexico at the time, and Mann believed the government failed to adequately check out Oswald's meetings especially what happened at this party. And the Thomas family believes he was demoted because he was aggressive in complaining about these alleged failures.
Frankly, I think there's nothing to this at all although I believe Silvia Duran, the Cuban consulate worker that Oswald met, has lied about her relationship with Oswald. Both Thomas and Mann were right to raise the questions as to who Oswald may have met in MC and what he did there; but they were shown, to me, to have no substance to them.
Here's a piece by Shenon that goes over the claims:
https://www.politico.com/magazine/story/2017/08/03/jfk-assassination-lone-gunman-cia-new-files-215449