Line an 8-inch square baking dish with aluminum foil; set aside.

In a medium saucepan, stir tamarind puree, sugar, and lime juice to blend. Cook over medium heat, stirring occasionally, until the mixture comes to a boil. Continue to boil until the mixture reaches 220°F on an instant-read thermometer, about 5 minutes. Remove from heat.

Add butter and stir until it melts; continue to cook for 5 minutes more. Remove from heat. Stir in pectin and cook over medium heat, stirring constantly, until the mixture thickens, starts to gel, and reaches 220°F, about 1 minute. Immediately pour the tamarind mixture into the foil-lined baking dish. Let cool at least 8 hours (or overnight). Cover and store in the refrigerator until ready to serve, up to 1 week.

When ready to serve, make one or more Fruity Sugars: Place 1 ½ ounces of freeze-dried mango, banana, and/or strawberry in separate resealable plastic bags. Using a rolling pin, pulverize each variety of freeze-dried fruit to a fine powder (you could also use a food processor). Transfer each fruit powder to a small mixing bowl and stir in ¼ cup sugar to each bowl. Repeat to create additional fruit coatings, if desired. If you like, make Tangy Sugar, too: Combine ¼ cup granulated sugar with citric acid in a small bowl.

Place a sheet of parchment paper on top of pan with tamarind pâte de fruit. Invert pan onto work surface; remove pan and foil. Run flat sides of sharp knife over the top of butter or spray with cooking spray to lightly coat. Trim uneven edges of pâte de fruit. Cut pâte de fruit into 1 ½-inch squares, running knife over butter as needed to prevent sticking. Alternatively, use a large round pastry tip to cut 1-inch rounds. If desired, use tip to cut rounds into crescent-moon shapes. Working in batches, roll the pâte de fruit pieces in your choice of Fruity and/or Tangy Sugars. Enjoy right away.