Using paint thinner will break down the paint, but it will also break down and damage the latex caulk. Scrubbing the caulking with isopropyl alcohol will remove the paint and leave the caulk intact.
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Soak two or three cotton balls with isopropyl alcohol and wet a small area of caulking that needs latex paint removed. Work in small areas as the alcohol dissipates quickly.
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Rub gently with a cotton swab soaked in alcohol. Use a scratch-free scrub sponge on thicker portions of paint. Scrape the surface of the caulk gently using a popsicle stick. Hold the stick at a 45 degree angle so as not to gouge the caulking. Use a toothpick to loosen any paint in the caulked corners.
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Mix ½ a cup of liquid detergent with hot water. Scrub the caulking vigorously with the scrub sponge. The remaining latex paint will ball up and is removable by plucking it off by hand. Scrub until the entire surface of the caulk is latex paint-free. Rinse with cool water and let it air dry.