It looks more like Carolina Buckthorn than Common Buckthorn. Carolina is a native plant, and its range extends into Texas. Common is an introduced plant, and it is especially invasive in the northern part of the country. Neither plant is especially good for deer, but they will browse them a little and eat the drupes. There are several other buckthorns, and all of them have about the same value when it comes to deer.
Common Buckthorn has 2 or 3 pairs of lateral veins per leaf, and the leaves are more oval shaped. I'm not seeing that in your plant. Those plant ID apps do an okay job on some things, but they are also sometimes wrong when it comes to the fine details.