We propose that periodically in space- and time-modulated potentials (dynamic lattices) can efficiently remove the excited (the high-energy and large momentum) components of the trapped Bose-Einstein condensates (BECs) and, consequently, can result in efficient cleaning of the BECs. We prove the idea by numerically solving the mean-field models (the Schrödinger equation for noninteracting condensates and the Gross-Pitaevskii equation for interacting condensates of repulsive atoms), and we evaluate parameters and conditions for the efficient removal of excitations.