Posting this here and anywhere else I can think of (and if you want to share, share!) because nothing that comes up on Google actually tells you how to do this - and since Tidy Networks (essentially a legal virus) came pre-installed on the brand new computer I got today I'd like to save other people from having to waste five hours fucking around trying to get rid of it since odds are it's going to be pre-installed on other machines.
First, you have to uninstall it from your computer. That's a pretty basic function in "settings" - just search "uninstall" and it will bring you to the area to uninstall it.
But that does not complete the uninstall. Unless you do the next step it will reinstall as soon as you turn your computer on and off.
What it does is attach itself as an extension to all of your browsers - this is what allows it to come back from the dead. So, once you uninstall you have to go to "tools" on your browser and then to "extensions" and then hit "disable".
If you do this after the uninstall it will be gone for good.
I'm sort of pissed that there is no way to know this without experimenting yourself. Every bit of "advice" on Google suggests you pay money to have a program get rid of it. Not only do you not need to do that, but it won't work as long as the code is hanging around in your browsers.
Anyway, if this saves one person from the five hours I fucked around with this it's worth it.