Mix turkey, salad dressing, tomatoes with green chile peppers, jalapeno peppers, onion, chili powder, and black pepper together in a bowl until turkey salad is evenly combined.
Stack tortillas on a microwave-safe plate and cover with a paper towel. Microwave until tortillas are warmed, 20 to 30 seconds.
Spread about 2 tablespoons turkey salad onto 1 side of each tortilla; top with Mexican cheese blend and lettuce. Fold opposing edges of the tortilla to overlap the filling. Roll 1 of the opposing edges around the filling in a burrito-style.