The American army drove the Mexican army all the way to Mexico City. The Mexican government in exile negotiated the Treaty of Guadalupe Hidalgo establishing the current boundaries of the United States southwest. We paid them $15 million compensation for damage to Mexican property. We didn't annex it. It was ceded in a legal, binding treaty with both governments.
I'd like to see them try to dispute a legal document.
Oh wait, what am I saying? They have no respect for the law and so would have no respect for a binding legal document.
(And they want us to respect them??)