How to remove dried latex paint from clothing

Try a heat gun, it will soften the paint and allow you to scrape it off more gently. Be sure to follow instructions for proper ventilation and material safety especially if there's any possibility of lead paint.

However, unless you're particularly in love with those tiles, tearing down and re-tiling will likely give you a better result in less time.

If the tub material is fiberglass (and most commonly are) the best way to remove any blemish is with an orbital sander and some 300 600 and 1000 grit Wet and Dry sandpaper. Using a spray bottle filled with water wet the stained surface. Starting with the lowest grit sand and keep the area wet. Let the sander do the work. No need for hand pressure. Watch how fast the stain is being removed (it should go quickly. Move through the grits and spray to keep surface continuously wet. The paper is of such a fine grit it will not leave any discernible scratches. When completed apply a cleaner/sealer for fiberglass.