Heat a large skillet over medium-high heat. Coat pan with cooking spray. Add steak to pan; sprinkle with 1/8 teaspoon salt. Cook 3 minutes or until browned, stirring occasionally. Place steak in a medium bowl.
Add butter to pan; swirl until butter melts. Add remaining 1/4 teaspoon salt, garlic, and mushrooms; cook 6 minutes or until mushrooms brown and liquid evaporates, stirring occasionally. Add mushrooms to steak; toss to combine.
Wipe pan clean with paper towels. Reduce heat to medium. Sprinkle about 2 tablespoons cheese evenly over half of each tortilla. Divide steak mixture evenly among tortillas; sprinkle with remaining 1/2 cup cheese. Fold tortillas in half over filling. Carefully coat both sides of quesadillas with cooking spray. Place 2 quesadillas in pan; cook 2 minutes on each side or until browned and cheese melts. Repeat with remaining quesadillas. Cut each into 4 wedges. Serve with marinara.