The correct answer is B) The U.S. took Texas without regard for Mexico's claims.
The fact that best illustrates the role of Manifest Destiny in the U.S. -Mexican War is "The U.S. took Texas without regard for Mexico's claims."
That is exactly what the Manifested Destiny was for the US President James K. Polk at that time. The idea he had was that the United States had the right to spread and gain more territory, despite other countries' claims. That was the case for the Mexican-American War that started in 1846 and ended in 1848, with a victory of the US and the signing of the Guadalupe Hidalgo Treaty that gave the US the territories of Utah, California, Nevada, New Mexico, and Arizona.