Heat deep-fryer to 375 degrees F or as recommended by manufacturer for similar foods. Deep fry wonton skins until golden brown and drain on paper towels.
Combine cucumber, tomatoes, and mayonnaise in a bowl and season with salt and pepper, to taste.
Spoon a small amount on each fried wonton triangle and top with 1/4 teaspoon tobiko caviar. Finish with a parsley sprig.