Combine 1 cup boiling water and tamarind pulp in a small saucepan. Let stand, covered, 1 hour, stirring to combine. Drain tamarind mixture in a sieve over a bowl, reserving liquid. Return solids to pan. Add remaining 1/2 cup boiling water, stirring to combine. Press tamarind mixture through a sieve over bowl, reserving liquid; discard solids.