I suspect a majority of the population has no idea what "Michaelmas term" is. And there's some other phrases in there that require some familiarity with things commonplace in the 19th century that aren't so in the 21st century.
Dickens had a lot of issues with the legal system at the time and it was a protest work.
Toward the end of the story the fighting does stop when lawyer's fees, which they had been charging to the estate, at last empty it. This is announced publicly in court, and the attorneys respond by flinging their piles of paper into the air, one of a few comic scenes in the novel.
FYA, this modus vivendi is still being practiced -- see the litigation around the estate of O.J. Simpson.
I suspect that the unfamiliarity with words like Michaelmas was part of the point.
I.e. What do the students do when reading a book and they come across a word they don't know? Look it up? Deduce it's rough meaning from context? Live with the uncertainty? Get mad and not finish the text?
In my defence, I'm not a native speaker