Pepe Garcia and Iris Kendall left their love back on the island it seems ... 'cause the two are through -- although, he says he didn't cheat like the internet's suggesting.

We caught up with the "Love Island USA" star in Beverly Hills on Thursday ... and, we had to ask him about his relationship status after he and Iris finished fourth in the most recent season of the show. Getty

Pepe says breakups are tough -- especially when all of show's fans have their eyes on you ... but, it's just the way this cookie crumbled it seems.

Then, Pepe straight up shoots down any rumors that he stepped out on Iris ... telling us there's no truth to the speculation. Getty

Garcia says he doesn't care what the internet or anyone he doesn't know thinks about him ... which is for the best, since hi

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