Rinse shrimp in cold water. Pat dry with a paper towel and set aside on a plate.
To make the marinade, in a small bowl, whisk together the tomato paste, water and oil. Add garlic, chili powder and oregano. Mix well.
Using a brush, spread the marinade (it will be thick) on both sides of the shrimp. Place in the refrigerator.
Prepare a hot fire in a charcoal grill or heat a gas grill or broiler. Away from the heat source, lightly coat the grill rack or broiler pan with cooking spray. Position the cooking rack 4 to 6 inches from the heat source.
Put the shrimp in a grill basket or on skewers and place on the grill. Turn the shrimp after 3 to 4 minutes. The cooking time varies depending on the heat of the fire, so watch carefully.
Transfer to a plate and serve immediately.