Remove the outer pod from the tamarinds, discard, and place the pulp in a bowl. Cover them with 2 cups boiling water and let them sit anywhere from 2 to 24 hours.
With your hands, clean then tamarinds of the large seeds and strains/threads. Strain in a colander, pressing with your hands or a spoon to get as much pulp as possible.
Place the resulting tamarind juice in a saucepan. Bring to a boil, add the sugar, and let it simmer over medium heat for 30 minutes. The juice should have thickened considerably, to a thick syrup consistency.
Squeeze in the fresh lime juice, let it simmer for a couple more minutes and let it cool. Refrigerate and store in a tight lid container. The concentrate will keep for months.