I remember a lot of fuss being made about these but, as time goes on, I'm very sceptical they can work. Looking at the Afghan data leak reported earlier this year: courts can make it practically difficult for most of the organisation to even know they're subject to court orders!
The person updating the website asks "have we received a court order?" and the person under injunction must answer "not me." The website author isn't lying, but the website contains incorrect information (as the result of a legally-enforced lie).
You could ask your lawyer but, once again, they'd also answer "no we haven't" because answering anything else is contempt of court at best.
I'd think the CEO would know, would they not? And the CEO could tell the person updating the website: "Let's go ahead and remove the canary, we don't need it anymore." --> "OMG, did we get secretly subpoena'd?" ---> "No, not yet, but I just don't want to run the warrant canary anymore."
The only way the CEO finds out is if they're made privy to the injunction, at which point they become subject to it. Even an oblique hint could be a breach of the injunction.
Be honest: do you think a judge is stupid enough to believe you had the injunction explained to you by your legal counsel then, in a totally unrelated incident, thought "oh, I don't think we need the warrant canary any more."
The person updating the website asks "have we received a court order?" and the person under injunction must answer "not me." The website author isn't lying, but the website contains incorrect information (as the result of a legally-enforced lie).
You could ask your lawyer but, once again, they'd also answer "no we haven't" because answering anything else is contempt of court at best.