"You stole our land and we want it back"

This is a phrase that illegal aliens have started chanting. Claiming that the United States had illegally taken over their territory such as Texas, California and Oregon and they want it back citing the treaty of Guadalupe Hidalgo.
I will admit that I am not a historian and that this was the first that I ever heard of this treaty, so I decided to do a little research and thanks to the Montery County Historical Society, I found a copy of the treaty which you can view at this link.

" The Treaty of Guadalupe Hidalgo, ending the Mexican War, was signed on February 2, 1848, by Nicholas P. Trist for the United States and by a special commission representing the collapsed government of Mexico. Trist disregarded a recall to Washington, and negotiated the treaty in violation of most of his instructions. The U.S. Senate reluctantly approved the treaty.
Under the treaty, Mexico ceded to the United States Upper California and New Mexico (including Arizona) and recognized U.S. claims over Texas, with the Rio Grande as its southern boundary. The United States in turn paid Mexico $15,000,000, assumed the claims of American citizens against Mexico, recognized prior land grants in the Southwest, and offered citizenship to any Mexicans residing in the area."

Again, I'm not a historian or legal expert and I will be looking into this in more detail after finals week, but from the jest of what I'm getting from this is that the United States and Mexico were at war and Mexico lost.

"they want it back", even for the sake of argument if these territories were returned, they would be returned to the Mexican government, not the people.

So I would take that under consideration before I make such a claim especially since the major reasons cited for being here is because of the lack of opportunities and tyranny from their homeland.