And Katie always drops her ticket when you try to bring her to a town that already has her or that had her earlier the same day, to prevent paradoxes. But it gets rid of her just the same as if you'd delivered her to another town, and you still get her reward in the mail the next day like usual.
If you haven't seen her do it before, when you try to bring her onto the train when going to a town that has/had her, she'll drop her ticket and get back off the train. Then the train takes you to the other town without her. But when you get back home, she's gone, and you get a letter the next day like normal.
I can loan you a megaphone. You can only use it when your gate is closed, so I can visit, drop it off, leave. Then you call Katie with it, come to my town, and give the megaphone back. Does that work for you? If so, I'll look for your gate.
And yes, Katie just wanders around the main part of town, never on Main St. And she shouldn't disappear except for at 6AM when a new day starts, and only then after she's been in your town for a few days.
Okay, my gate is open for you again now. And I have a bunch of free items laid out by my train station, so you can take as many of those as you'd like.
I have these items out for all visitors to my town. And they're free. And if you don't want any, you don't have to take them. And you already did me a favor by letting me get rid of Katie.