We show that portions of an image written into a gradient echo memory can be individually retrieved or erased on demand, an important step toward processing a spatially multiplexed quantum signal. Targeted retrieval is achieved by locally addressing the transverse plane of the storage medium, a warm Rb-85 vapor, with a far-detuned control beam. Spatially addressable erasure is similarly implemented by imaging a bright beam tuned near the Rb-85 D-1 line in order to scatter photons and induce decoherence. Under our experimental conditions atomic diffusion is shown to impose an upper bound on the effective spatial capacity of the memory. The decoherence induced by the optical eraser is characterized and modeled as the response of a two-level atom in the presence of a strong driving field.