You are correct, the correct title for this topic if anything should be Vario gave up Tommy DeSimone because he raped Karen Hill. Vario and the Lucheses didn't kill DeSimone, the Gambinos, most likely Tommy Agro, killed DeSimone because he killed Batts. DeSimone was an earner but he was also a cowboy, as Paul Sorvino said in the movie. Once he outlived his usefullness he was expendable, no different than DeMeo or Sam DeSefano in Chicago, eventually lunatics get too hot. Once Vario got tired of the Fatico crew and the Gambinos hassling him about what happened to Batts he probably figured that DeSimone wasn't worth it. Throw in the fact that he had a thing for Karen Hill most likely Vario said thanks for the memories but I am turning you over to the Gambinos, have fun getting shot in the face.