This question was inspired by one about whether the public in the Galactic Republic knew Count Dooku was a Sith Lord.
At the start of the movie, the Jedi still thought very highly of Count Dooku even though he left the Jedi Order.
MACE WINDU: You know, M’Lady, Count Dooku was once a Jedi. He wouldn’t assassinate anyone, it is not in his character.
KI-ADI-MUNDI: He is a political idealist, not a murderer.
By the end of the movie, they knew Dooku was a killer.
The Jedi learned that a Sith Lord named Sidious controlled the Senate from Count Dooku.
Count Dooku: What if I told you that the Republic was now under the control of a Dark Lord of the Sith?
Obi-Wan: No, that's not possible. The Jedi would be aware of it.
Count Dooku: The dark side has clouded their vision. Hundreds of senators are now under the influence of a Sith Lord called Darth Sidious.
The Jedi didn't believe it at first, but by the end of The Attack of the Clones, the Jedi decide to watch the Senate.
Kenobi: Do you believe what Dooku said about Sidious controlling the Senate? It doesn't feel right.
Yoda: Joined the Dark Side Dooku has. Lies, deceit, creating mistrust are his ways now.
Mace: Nevertheless, I feel we should keep a closer eye on the Senate.
Yoda: I agree.
Once the Jedi were forced to rethink their views on Dooku, why didn't they tell the public?
They could have told the public, "Hey, that Confederacy of Independent Systems you want to join? It's controlled by a man who has ordered the deaths of thousands of people. He's not just a man who left the Jedi Order, but has become very corrupt who will use lies and deceit to destroy the Republic."
They could probably back up their words with video footage of the Battle of Geonosis; video footage showing Count Dooku watching the slaughter of Jedi knights within the arena. (Assuming the clones has body cams, and that their attack ships had cameras.)
To my best knowledge, the Jedi never told the public that Count Dooku had gone bad, and that a Sith Lord controlled the Senate. By going public, they could have:
- undermined confidence in Dooku's leadership,
- dissuaded planets from joining his CIS,
- and gotten the public to turn a skeptical eye toward the Senate.
All of these outcomes would serve the Republic and undermine the Sith Lord's plans. So why not go public?
Edit to add: To my best knowledge, the Jedi didn't learn until episode, “The Lost One” (The Clone Wars, S6:E10), that Count Dooku is not just a fallen Jedi but a Sith Lord as well. So once they learned that, they could have also told the public, "Count Dooku is a Sith Lord. History says that each time a Sith Lord tried to create an empire, he ended up causing the deaths of millions or billions of people."