Most of the American Southwest was won in the Mexican War and ceded to the US in the Treaty of Guadeloupe Hidalgo. Later a strip of what is now southern Arizona was purchased, the Gadsden Purchase, intended to allow a railroad route to San Diego. It wasn’t stolen and only some of it was purchased. Either way it’s ours and we are not giving it to anyone.
Gadsden Purchase was a separate treaty of sale, several years later.
Treaty of Guadalupe Hidalgo gave the Mexicans $15 million, plus agreed to pay up to another $5 million to settle the claims of Americans against mexico.
We bought it with blood AND gold...then bought more for only gold.