We did better than that - out of Christian guilt we paid them for it, when really there was no reason to.
He implies that the $15 million was chump change but that was actual dollars in 1846 - corrected for inflation it was billions. It helped the Mexican Republic with their debts.
There was opposition to the Mexican War in the U.S. (Lincoln and Thoreau being famous cases) so this was a political sop to them.
We paid the same amount for the Louisiana Purchase and a bit over $7 million for Alaska.
The government made better deals in those days.
If the Mexicans want the land back, declare war and fight us for it! (In a way they have, I know)