Peppervine, "Ampelopsis arborea" is considered an invasive plant species even by the Lady Bird Johnson Wildflower Center, but there is little that I can find about methods of control. It apparently prefers a good, healthy soil that is evenly moist, just what most turf grasses also prefer.
Check with your local office of the Texas A & M Cooperative Extension Service about control measures.

Here is a link that might be useful: TAMU CES