First, I am going to say I have no experience in removing this stain, but the composition of an alkaline dry cell battery offers some clues. The battery consists of metal oxides (zinc and manganese) and potassium hydroxide. It is alkaline, not acid. The stains are basically what you describe, rust stains, but probably not iron oxide. Normally, metal oxide stains are removed by acid reduction using oxalic, muriatic, phosphoric, sulphonic or other acid materials. The problem here is that your pool plaster has a high marble dust content that can be severely damaged by acids, not to mention, you really can’t do this underwater. Oxalic acid or acetic acid (vinegar) are the only materials that might work and not harm the plaster, but your should obviously test this first.
Try to scrub the stain using a stiff brush or even a metal brush. Also, talk with the company that did the replastering to get their blessing for any cleaners you use and, if all else fails, estimates for repair / recovering the affected area.
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