Captain Kirk was in a short but deeply heartfelt relationship with a woman who then died. It affected him so deeply that Spock and McCoy got together and decided that the best thing to do was to use the Vulcan mind meld to erase all memory of her from Kirk's mind....at a time when Kirk would not be aware of what Spock was doing. And they would also take the step of altering the Enterprise's memory banks as well, to remove all trace of her so that Kirk would not find out anything about her by accident.
Not quite. As the passage quoted above shows, the mind meld in "Requiem for Methuselah" was entirely Spock's unilateral decision, even if McCoy did inadvertently give him the idea. And there's nothing about altering the memory banks.
It's also quite ambiguous about what "Forget" meant, since it was the last line of the episode and of course there was no followup. We don't know for a fact that Spock actually erased all memory of Rayna. He could've just meant to help Kirk "forget" the intensity of the pain he felt. I'm reminded of the research in real life pertaining to drugs that can prevent post-traumatic stress
by affecting the formation of negative memories. They wouldn't really remove the memory of traumatic events so much as soften it, make it less overpowering. You'd still remember the overall experience, but the bad parts would be vaguer, easier to move beyond.
There is an old Trek novel called Cry of the Onlies
that brought back Flint and did assert that Spock had repressed Kirk's memories of Rayna altogether, but as far as I can tell from the samples in Google Books, there's nothing there about the ship's databanks being altered. Which makes it rather less credible, since surely Kirk would review the mission logs afterward and would notice if they mentioned the existence of a woman he didn't remember encountering. Which supports the idea that Spock just made Kirk forget the depth of his feelings rather than her very existence.