We demonstrate the destruction of attractors in the logistic map with time delayed feedback by means of a weak harmonic modulation applied in different ways. The ability of the method to select a desired state is illustrated through codimensional-two bifurcation diagrams in the parameter space of the frequency and amplitude of the control modulation. We compare the efficiencies of different kinds of the open-loop control in annihilating attractors, in particular, when the modulation is applied to a feedback variable, feedback strength or multiplicative parameter. The comparative analysis shows that modulation of the parameter is the most efficient way for destroying the attractors.