Stir together the Greek yogurt, salt, white vinegar, and lime juice. Transfer to a squeeze bottle and refrigerate until ready to use.
Melt butter in a skillet over medium heat and cook the garlic and ginger until fragrant. Add the tomato paste, spices, and crushed tomatoes, season with salt, and simmer for 10 minutes. Blend smooth with an immersion blender, stir in the heavy cream, and keep warm on low heat. (If using tomato sauce instead of crushed tomatoes, skip the blending step.)
Cook the chicken tenders according to package directions until golden and cooked through.
Toss the cabbage, cilantro, lime juice, honey, and salt together. Char the tortillas directly over a gas burner or in a dry skillet on high heat, about 20-30 seconds per side.
Add the slow to a tortilla, then add the chicken tender on top, tikka masala sauce drizzled over, cucumber slices tucked in, Greek yogurt zigzag from the squeeze bottle, and fresh cilantro. Serve immediately with extra sauce for dipping.