Dice the cucumber into 1/2-inch pieces and dice the tomatoes, placing them in a medium bowl. Add the shredded romaine lettuce, crumbled feta cheese, dried oregano, and a pinch of salt. Drizzle with fresh lemon juice and gently toss everything together until well combined. Let this sit for a minute to allow the flavors to meld slightly—I find this brief rest helps the vegetables absorb the lemon and oregano better than if you assemble right away.
Lay out one flour tortilla on a clean work surface. Spread approximately 2 tablespoons of roasted garlic hummus across the lower half of the tortilla, leaving about an inch from the edges. Top the hummus with 2.5 oz of cooked chicken strips (roughly 1/4 of the total), then spoon about 1/2 cup of the vegetable mixture from Step 1 on top of the chicken. I like to keep my fillings in the lower portion of the tortilla and not overstuff—it makes rolling much easier and prevents ingredients from spilling out.
Fold the bottom edge of the tortilla up and over the filling, then fold in the left and right sides toward the center to create a seal. Roll the tortilla tightly away from you into a wrap, keeping the seam on the bottom. Place seam-side down on a serving plate or cutting board. Repeat with the remaining three tortillas and filling. For easier eating, you can slice each wrap in half diagonally if desired.