Mexico never ruled the American southwest. Comanches did until the Texans came to Texas. Mexico has no claim.
Especially after Santa Ana became dictator under the Plan of Cuernavaca in 1834.
The plan contained five articles:
Repeal the Ley del Caso and do not tolerate the influence of Masonic lodges.
Declare void the laws passed by Congress and the local legislatures.
Request the protection of President Santa Anna to fulfill the plan, and recognize it as the only authority.
Remove from office the deputies and officials who carried out enforcement of the reform laws and decrees.
Provide military force to support the president in implementing the plan.
The plan was followed a week later by the "Plan of Toluca", issued by the garrison of the State of Mexico, which threw out the governor and the federalist state legislature.