Answer: c. They hoped that international recognition would pressure Mexico to give up its claims to Texas.
Step-by-step explanation:
Even though Texas had won their war of independence against the Mexicans, the Mexicans did not regard them as independent but rather as a breakaway province that would simply rejoin Mexico eventually.
The Texans knew this and sought to thwart it by seeking international recognition because they knew that this would pressure Mexico into giving u its claims because a sovereign nation recognized by others would be less likely to be treated as a breakaway province.