Well, the flaws of interstellar invasion as a concept aside, what there is for taking? Almost any rescues are cheaper available in space than on inhabited planet with heavy atmosphere.
So much to remind that automated asteroid mining is how advanced civilization is getting ore, pretty much any of it. Even organic compounds, to some degree, from comets and interstellar clouds.
And short of wormhole "stargates" you don't haul much stuff around planet to planet anyway. Now, that may be a whole reason to set up local infrastructure indeed, but your macguffin they're after here better to be biological.
We have to assume the ecology is at least somewhat compatible, then there's the simple potential for a colony, as living space to grow into or outpost to explore further from, or just to split and ensure their own resilience.
The only other resource worth planning the overtaking of Earth is likely the humans themselves, and even then there's no actual reason to ask. Few dozen abducted humans set to reproductive duty full time can grow into billions within a couple centuries (the math of maxed out human growth is somewhat shocking, and that's even before one considers clones and/or artificial wombs). So if there's marketable demand for human pets, it probably easier to breed those in-house anyway.
Of course, greed and impatience being how they are, it's perhaps somewhat interesting to deal with the existing population...
And the question was, what someone does with evidence aliens manufactured the crisis they offered the help for? Hey, wouldn't that be the default assumption anyway, at least among certain parts of society? Anyway, there's certainly those who hate the aliens no matter how lovable they may appear, so there will be nutcases willing to listen. The problem behind, they're likely nutcases.
A lot depends on what the known relevant plans for humans are under the alien regime.
The pragmatic, the governments, the undefinable "majority" may not be as willing to listen. Even, let's face it, if a random person figured it out, the institutions crafting deals with aliens likely know already. Know and don't care, for reasons as personal corruption.
And corruptive opportunities for aliens enslaving Earth are almost unlimited. Don't underestimate the power of short term desires of individuals...
Also, spreading around the alien interstellar empire as pets may be just the chance we need to get off this rock. There's no shortage of willing slaves, never was.
That they lied to us, is hardly news. It has to be expected. The more relevant question is, what their plans might be? And what we can do to resist the worst. If they already demonstrated that they can wipe us out, but then offered collaboration, it's kind of stupid to refuse the survival chance, whatever the price. As long there's belief it isn't just short term abuse before finishing off with us. Even then, it's opportunity to learn, learn about them, their plans, abilities, technology.
Full out war may be a suicide. Resistance movement has to plan for a long haul, eventually centuries. It can and has been done in human conflicts, although such are rarely explicitly planned.
With outright aliens, as long as they're not telepathic, it's even easier, just as we don't understand them, they can't fully understand all we do, and have to live with it. All we have to is concentrate on preserving the lore, and seeding the dream of regaining independence, on the next level in par with our new masters.
So what to do with evidence we have been tricked into the situation? Spread the word, as cautiously as possible, preferably on peer networks. If/when there's reasonable backup and if they're gaining support in positions of influence, it may not be out of question to negotiate. Careful, no sudden motions. If aliens went to such lengths in the first place, a major uprising might not be in their interests. They may offer concessions, personal or otherwise, just to keep quiet and control. The long game is gaining equal rights in their kingdom.