In a small bowl, whisk together ketchup, mustard, dill pickle relish, and Worcestershire sauce. Set the burger sauce aside.
Heat a large skillet over medium-high. Add ground beef and diced onion; cook, breaking up the meat, until browned and cooked through, about 6 to 7 minutes. Drain excess fat.
Season the beef with garlic powder, onion powder, salt, and pepper. Reduce heat to low and cook 1 minute to bloom the spices. Remove from heat.
Warm tortillas until pliable: wrap in a damp paper towel and microwave 20 to 30 seconds or briefly heat in a dry skillet.
Assemble each wrap: spread a spoonful of burger sauce over a tortilla. Add a quarter of the beef mixture, then top with shredded cheddar, lettuce, and tomato.
Fold the sides in and roll tightly like a burrito, placing the wrap seam-side down.
Lightly oil a skillet with neutral oil and heat over medium. Grill wraps seam-side down until golden and crisp, 1 to 2 minutes per side, until the cheese melts.
Slice in half and serve with extra sauce for dipping.
Notes
Swap ground beef for ground turkey or plant-based crumbles. Add cooked bacon for a deluxe version. For spice, mix 0.5 tsp hot sauce into the burger sauce.