Is releasing this company's documents illegal?
Yes.
I run a website where I sell materials for students interested in finance, law and consulting.
My website contains case studies from actual previous interviews.
[from comments: I sell the literal documents that the company gives candidates who are interviewing.]
Those documents are (presumably) written by those companies.
They automatically own the copyright to those documents.
Copyright law forbids distribution of copyrighted works, unless you are the copyright holder, or have a license to do so.
Neither applies to you, so your distribution of these documents is illegal under copyright law.
Since you are selling these documents your infringement is of a commercial nature.
That makes things worse for you, since it's harder to claim you were unaware the works were copyrighted, and the sentence may be more severe.
Recently, one of the firms' HR reached out regarding one of my case studies and asked me to take it down.
So take it down, and apologize profusely.
The case study is just a word document and an accompanying excel file that contains no indication of confidentiality.
Irrelevant for a copyright claim.
[from comments] They do own the case study but I don't know that they copyrighted it.
Irrelevant.
Copyright is granted automatically; they don't need to tell you.
You are required to know the law, and will be prosecuted as such.
My question is, am I required by law to take the case studies down?
Yes.
What are the consequences if I do not?
They can sue you for copyright infringement.
I'm willing to bet money on them winning that case.
If they do win, you will likely be ordered by the court to stop distributing the materials, and to pay (punitive) damages to the prosecutor.
Edit: I just got an email from Kirkland and Ellis on behalf of their client with a letter titled "Cease and Desist - Fraudulent/Illegal distribution of [company's] confidential and proprietary information". I immediately took the materials off the website. A few questions on next steps:
Am I in the clear now?
No, they can still sue.
You took them down now, but what you did was still illegal.
Hence my advice to apologize to them profusely, to hopefully dissuade them from pursuing legal actions.
Can I get a lawyer and try to fight this (i.e Kirkland's charge against me)?
Yes. You can get a lawyer for pretty much anything.
You shouldn't, because you'll lose and make things worse for you.
Should I take other companies' materials down as well?
Yes.
What happens if I don't?
They can sue, and likely win.