As a follow up, was there regime change in Mexico afterwards? It seems like the US has a history of paying for part of damages after regime changes such as Iraqi Freedom and The Civil War (reconstruction)

Was it paid for damages, or for annexing Texas?

The short answer is that the Mexican-American War was started due to the United States annexing the Texas Republic (which had been "independent" according to much of the world from 1836 to 1845). Mexico never ratified either version of the Treaty of Velasco. The public version had Santa Anna, the Mexico President who had been forced to sign after being captured, moving Mexican troops south of the Rio Grande (roughly the border of Texas terrorize when it was part of Mexico). The secret version had Mexico recognizing Texas' independence. Mexican soldiers sporadically crossed the border and attacked Texians and Tejanos.

Texas' claim was grand. They claimed Mexico north of the Rio Grande, but how far west. The United States offered to pay Mexico for the territory west of what was obviously Texas to the Pacific. This included present day New Mexico, Arizona, and California. No one really thought Texas could legitimately claim all of this land (Unless you were a supporter of Mirabeau Lamar), but the United States had its eye on it. Fighing continued over the land rights of California etc. The United States won and took the spoils of war. In exchange, Mexico received money for the "lost" territory and paid for damages. Without such a large land exchange, I doubt the the victor would not have paid for physical damages and citizen debts.

For some Mexicans, they felt that Mexico was too large to administer. The loss of these sparsely populated territories with very few natural resources (jokes on Mexico during the 1849 Gold Rush and silver rush in the Rockies in The 1850s).