With the One-Punch Man manga's most anticipated fight between Garou and Saitama now behind it, it turns out that there's only one character who actually remembers what happened--and it isn't either of the combatants.
The battle between Garou and Saitama was initially fairly one-sided since Garou desperately wanted to fight and Saitama wasn't all that interested. Garou figured out one way to finally force Saitama to get serious, however, and that was by killing Genos and ripping out his core, which seems to function as both brain and heart to his cyborg body. Saitama and Garou's battle escalated rapidly from there, with portals, deadly radiation, the warping of spacetime, and Saitama destroying Jupiter and Io with a sneeze. The fight ended when Saitama actually transcended causality, throwing a punch that landed hours before it was thrown and soundly defeating Garou before any of that could happen.
This briefly led to there being two Saitama in chapter 169 of One-Punch Man--the one from the future who landed the punch, and the one who existed at that time and was still lost amongst the rubble of Monster Association HQ. They were quickly integrated back into one being, a Saitama with no memory of that battle in deep space but who was still holding Genos' core all the same. Since this took Saitama back to before Genos was killed, he found himself looking at the badly injured but still alive Genos before Garou killed him, little more than a torso and a head. Intrigued by the duplicate core, Genos connects with it, and immediately witnesses everything that happened in the alternate timeline, including the fight that occurred while Saitama was carrying that core. Since the future Garou was destroyed by God as a consequence of failure, that made Genos the only one to know the truth. While Saitama legitimately doesn't remember, Genos assumes that he's once again being modest about his achievements, as he did back in the fight versus the Deep Sea King to avoid ruining the reputation of the other heroes like Mumen Rider, who had fought bravely and lost.
Time travel can be a risky proposition for a story, as it runs the risk of making the conflict seem pointless when both victories and defeats can be easily undone. Having only one character remember is a fairly common way to handle that problem, but One-Punch Man has taken it a step beyond that. Saitama had major realizations about being a hero during that fight, like acknowledging that his late arrivals led to a lot of suffering that wouldn't have happened had he been faster, or realizing that his desire for a challenge was a bit selfish, having now seen the consequences of someone powerful enough to give him trouble. But while that might've been the first time he said these things out loud, the former, at least, was clearly a thought that had been weighing on him for some time. Genos' memory of those events allows him to say the perfect words to raise Saitama's spirits: "you showed up just in time."
This one line does a lot to ensure that the emotional weight of that fight wasn't lost and helps to keep the time travel from feeling like quite as much of a cheap solution. Genos and Saitama's relationship will always be the "core" of One-Punch Man's story, and this knowledge is sure to shape that friendship moving forward.