I have a problem with a black polo shirt

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When i took it out from the laundry machine to hang it to dry, i saw some white dots and marks. It looked like unrinsed soap that has dried on the shirt, so i handwashed it (rinsed) and the white marks went away. However, when the shirt dried, there are the white dots and marks again. I don't know what have caused this problem and how to solve this. This black polo shirt, Polo brand, is a favorite of my husband. Help!