I know I missed the "get your comment on the podcast" window, but I've got to come in and be a sourpuss, because this story really hit a pet peeve of mine. That is to say, stories about time travel that assume an anthropocentric cosmos without actually dealing with the consequences of that assumption.
Let me try to explain: you are particles. Your particles have location, energy, and arrangement, and that is why you are you and not, say, a rock, or a guitar, or a slowly expanding cloud of Hydrogen gas, or whatever. As you go around in the universe, you interact with other particles, which is what causes things to happen to you.
From the perspective of the universe - assuming a mechanistic, rationalistic, scientific universe - none of these particles are particularly important. It doesn't really matter if a particle is in you, or in a rock, or in a guitar, or in Jimmy Hoffa, or in Adolph Hitler. It's a particle. It moves around, bounces off of things, interacts with other particles... whatever.
Once you travel through time, you are going to interact with a HUGE number of particles. If you are in the past, with every step you take, you are going to send particles bouncing in every goddamn direction. This is often called the Butterfly Effect, the idea that the tiniest action can have far-reaching consequences.
At the same time, remember... the universe doesn't care. Miley Cyrus's particles aren't more important than my particles just because she's famous. Even though her actions have the ability to impact many more people - and all the particles they're made of - that impact is still orders of magnitude smaller than the impact she has by just walking around and having a body, to the point that on a universal scale, it's negligible.
In other words, if the universe isn't fundamentally human-centric, there is no reason for any sort of self-correcting phenomenon in time. The time stream or whatever isn't going to care more that I went back in time to kill Adolph Hitler than it does if I went back in time to kill some guy named Joe, or a cow, or shot a bullet at a rock. Give or take a (relatively) few tiny blips of matter, all of those actions are going to have the exact same impact. So, in a scientific universe, either time travel is possible and anything goes, or it isn't possible at all. There shouldn't be any half-measures, and there certainly shouldn't be any sort of "self correcting" around "important" events.
Or...
Maybe this isn't an entirely rational universe. Maybe this is a universe in which there IS a sentience that is in charge of the time stream that is willing to allow a few particles to be knocked around here and there, but has decided that certain human-scale events are just way to important to allow them to be changed, so it is constantly reaching in and redirecting the particles to make sure that nothing big changes. That's fine, I don't care, it's your story, write what you like.
But...
If you DO write your story that way, you are basically providing your world with scientific proof of God, or something very much like God. And in this story, God decided that our civilization has to be destroyed, our planet warped into an alien ecosystem, and our genes mingled with said aliens to produce a new species.
Which is fine... but it just bothers me that the story never goes there. If the alien girl had said "we can't change it because God won't let us, but at the same time I can come back and observe you because God will clean up all the little messes my presence causes," that would be fine. That would hold together. But the story as it is just leaves an enormous logic gap that I can't get past.
I'm sorry... I really envy all of you who were able to enjoy this story, because it was interesting and well written... but I just can't get it to work in my head.