But it’s pretty much the same as Mexico’s claim to the U.S. southwest. They had it for 27 years and we’ve had it for 169. But it’s really theirs.
And as to actual control, it was much less than that in many places. In the case of Texas, it was a mere 4-years.
Mexico gained control from Spain in 1821, but the Mexicans couldn't handle the Comanche and had to (like Spain had agreed to before) have Stephen Austin lead Americans there in 1825 to settle the area.