Whether or not she had violated the ZAP by the mere act of accepting a food service job is dependent upon her state of mind concerning the accuracy of the doctors' claims that she was a carrier. Keep in mind that she was the first example in recorded medical history of a completely asymtomatic carrier, and medical science was even less respected at that time than it is today. How many people whole-heartedly believe that the medical institutions have suppressed the cure for cancer or the risks of vaccines in order to sell drugs and vaccines? It's not at all unreasonable to believe that Mary believed she was being unfairly persecuted, and perhaps even without cause. She was neither the only typhoid carrier at the time (once it was known, many were identified, roughly 3% of survivors were asymtomatic carriers) nor the only one to break the terms of their quarantine release, but the only one to spend the rest of her life in quarantine. She wasn't even the most deadly in that same decade.
Some of the most heinous actions in history have been perpetrated by people thinking they were doing good, or even that it was god's will that they do what they did. Intent to do wrong is not necessary to do wrong.
And restitution for what, exactly? She may have caused harm, but again only passively. A judgement of restitution, even if it were just to impose upon Mary for the events prior to her first encounter with the public health agents, would effectively be a form of slavery. She literally had no knowledge or control over the harm caused, at least prior to her first arrest. It's a leap of logic to presume that she intended to cause harm, certainly befor the first incarceration, which lasted for about five years IIRC. Even showing harm caused was difficult at the time.
Again, intent is not necessary for you do to harm. If you do harm, you're liable for the damages. You may not have meant for the baseball to go through your neighbor's window, but it happened, and you still owe him a window.
You can make the argument that a heroin addict can be held responsible for the harm he causes others while high, or for the crimes he might commit in persuit of his addiction. But how can you make the argument that the heroin addict should pay restitution to the stupid kid that sees the heroin addict and thinks it can't be that bad, and then gets addicted himself?
This would make sense if she had not directly caused the harm that she did. She spread disease not only by being a carrier, but by not washing her hands before prepping food. She didn't have to work in food service. In fact, in her first quarantine, cultures of her waste showed that she was "teeming with typhoid salmonella", and she ignored that fact.
In hindsight, there was many things that Mary had done to earn her quarantine. But that's exactly the problem that I see. We have the benefit of both that hindsight and the common knowledge gained from those events. But what if we didn't? What if New York state was an ancap society in 1907? How could the actions that were taken have been justified at the time? (retroactive justifications are always false arguments, if you can't make the claim at the time then you can't make the argument later) If such actions cannot be justified under an ancap society, and I can't see how they could, what would an ancap society have been able to do to respond to the (general) threat of unaware & passive carriers of infections, and still remain an ancap society? If a special medical institution had the special power to incarcerate people under the charge of being a passive threat to society, wouldn't that same institution then have the monopoly on force that defines a modern government?
No. They would have the ability to use force, but not a monopoly. And that's the key factor.
Once the presence of the typhoid bacteria is proven, continuation of her actions is not a "passive threat to society," it's a direct attack. Regardless of whether she thinks she's doing it or not, she's directly harming anyone she cooks for, because she refused to take simple health precautions.