This is what the SL Encyclopedia sez:
“Eye For An Eye”/ “Occhio per occhio” (Gaspari-Nohra-Morricone) Tie-in single (7” vinyl ARC AN 4083) released in Italy in 1967 to take advantage of the popularity of For a Few Dollars More, it used Morricone’s main theme as the setting for some impassioned crooning by Maurizio Graf . The A-side English version was in stereo, the B-side was in Italian mono. Currently available on the expanded edition of the Italian soundtrack CD (GDM 2038). The English lyrics are by M.G. Gaspari and Audrey Stainton Nohra.
Sounds to me like the song was manufactured after the fact. Single and album tie-ins were popular with entertainment companies at the time: it was a way to get punters to put up money twice, once for the film, and once for the record. Often a production would squeeze in a number in the middle of the action to spotlight the song (a character would sing it in a club or whatever), but sometimes a film's title music would do, especially if it had lyrics. The movie would promote the single and vice versa. Of course, in some films it was impractical to get a song with lyrics into the production. I think in the case of FAFDM the film was so popular in Italy that the media people couldn't resist trying to milk it for extra scratch. FAFDM came out in 1965, but the single didn't appear until two years later: I'm guessing the producers didn't expect the film to be so popular, and when it was, they had to scramble to put something together so they could continue to bilk the public.