Let's go over the options:
- Copyright is out of the question as you cannot copyright an algorithm. No code is shared in this case anyway.
- Patent might be possible but the cons outweighs the pros in this case. Depending on the nature of your algorithm and your jurisdiction you may not succeed. And a patent by definition is going to disclose the algorithm to everyone, which is against your objective.
- Trade secret is your way to go.
my employee might have thought it was okay to share this information
publicly when it is absolutely not
Surely there was a non-disclosure clause on the employment contract? Now is the time to use it! You'd wish to establish that:
- The algorithm is "confidential".
- The employee leaked this confidential information and violated the NDA.
- There are damages to your company due to this action.
It's not as simple as it sounds though. Is everyone well aware of what they can and cannot share? Can you conclusively proof a certain employee is responsible? In some jurisdictions, if the company dismiss the employee without proofing their wrong-doings, the company may be liable under employment laws.
Should we go ahead and license it? Should we even talk about this on
our company blog?
Well, if you don't want somebody to notice it, don't talk about it.
In addition, if you wish to take down the content, you first need to establish you have the right to do so. It's more complicated when the website is hosted overseas.
TLDR: Your company would need to hire legal services. If the algorithm is valuable, the cost would be justified.