The structural reorganization of a phase-separated binary mixture in the presence of an annealed dilution of active impurities is studied by computer-simulation techniques via a simple two-dimensional lattice-gas model. The impurities, each of which has two internal states with different affinity for the two species, become active by an external driving of a transition between the two impurity states, leading to an energy flow from the impurities into the binary mixture. In steady state, the drive is found to break down the phase-separated state and lead to a new finite length scale controlled by the drive. The model can be extended to describe compartmentalization of biomembranes by active membrane-bound proteins.