Make the pico de gallo by placing the tomatoes, onion, cilantro, jalapeño, lime juice, and salt in a medium bowl. Stir to combine, cover, and refrigerate until ready to use.
Pat steak strips dry with paper towels.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat.
Once hot, add the steak to the skillet, spreading out evenly in a single layer. Sear the steak for 2 minutes before flipping.
Season the steak with taco seasoning, chili powder, and salt.
Toss to coat and continue cooking for another 2 minutes or until the steak is deeply seared and tender. Remove from heat.
To build a quesadilla, lay a tortilla out on a clean work surface.
Place approximately ⅓ cup of grated cheese on the bottom half of the tortilla. Repeat the process with all four tortillas.
Divide the steak between the tortillas, placing on top of the cheese.
Top the steak with approximately 1 heaping tablespoon of the pico de gallo.
Evenly distribute the remaining cheese on top of the steak of each quesadilla, and then fold the tortilla in half.
Brush both sides of each quesadilla with the remaining olive oil.
Heat a large skillet or griddle over medium heat.
Once hot, carefully transfer a quesadilla to the skillet or griddle, and cook for 2 minutes per side or until golden brown crisp on the outside and melty on the inside. Repeat until all quesadillas are cooked.
Slice the quesadillas into wedges and serve with the remaining pico.