An unsettling combination of a small child and an old man, this Ghost takes Scrooge on a tour of his past Christmases in order to reconnect him to his feelings.
The Christmas ghosts have distinct personalities; they're not all just the same kind of phantom presence. This ghost is generally quiet, thoughtful, and surprisingly compassionate for the bits of Scrooge's miserable childhood that we get to see. It makes sense that because there was actually a time in the past when Scrooge wasn't the horrible monster that he is in real time, the memory ghost doesn't go full out with blame.
What really separates each ghost from the others, however, are the weirdly surreal supernatural bits that Dickens invents for how they eventually disappear. The Ghost of Christmas Past, for example, is a lot like an old-timey candle. It comes with a cap that Scrooge keeps wanting to put on its head. But the ghost protests that putting this cap on will "extinguish" it and that memories need to be looked at rather than snuffed out.
But eventually, that very thing is what happens:
[Scrooge] turned upon the Ghost, and […] wrestled with it.
"Leave me! Take me back. Haunt me no longer!"
In the struggle, if that can be called a struggle in which the Ghost with no visible resistance on its own part was undisturbed by any effort of its adversary, Scrooge observed that its light was burning high and bright; and dimly connecting that with its influence over him, he seized the extinguisher-cap, and by a sudden action pressed it down upon its head.
The Spirit dropped beneath it, so that the extinguisher covered its whole form [...] (2.147-150)
It's actually pretty shocking that Scrooge suddenly wrestles with the ghost, isn't it? Why do you think Dickens decided to end the part of the haunting this way? Why doesn't the ghost just melt away on its own? Why doesn't it fight back against Scrooge? Does it make sense to make the ghost of memory function like an extinguishable candle?
Okay, okay, enough questions. We'll throw out one theory for you. Scrooge has lived a very long time repressing all of those horrible and painful memories to the point where it takes an outside supernatural force to make him relive them. It kind of feels like this extinguishing fight is a dramatic acting out of what Scrooge must have been doing all along in order to turn into the miserable monster that we find at the beginning of the story.
There is one literal ray of hope though—that even when the cap is all the way on the ghost, there is still some memory light shining out the bottom, meaning Scrooge will no longer be able to just forget everything about himself all over again.