In a mixing bowl, combine the drained tuna and softened cream cheese. Blend until smooth and well combined.
Add the Greek yogurt and chopped hard-boiled eggs to the tuna mixture. Stir until fully mixed.
Heat a skillet over medium heat and melt the butter.
In a separate bowl, whisk together the egg whites and optional xanthan gum until smooth.
Pour 1/4 of the egg white mixture into the skillet. Cook until the bottom is golden brown.
Flip the egg white wrap and cook the other side until browned and fully set. Remove from the skillet and set aside.
Repeat the process to make a total of three wraps.
Spread a third of the tuna salad mixture down the center of each egg white wrap. Fold the edges of the wrap over the filling to enclose it.
Serve immediately and enjoy your carnivore tuna salad wraps.