I go to the store and buy deionized, distilled water in gallon jugs. Cut the top from the jug and set the lens down in there and swish it around and then let it soak for several hours. Pat or very gently rub it dry with a soft, microfiber towel. Let the lens set in a dry, place out of the light and dry overnight. Then, using a commercial lens cleaner intended for delicate optics and using real lens tissue, go over the lens and in particular the "spots" and if at that point they are still there --then--what you have is an etched area in the coating or lens glass that is permanent.
I try to rinse my lens after a dive but I do not leave my camera banging around in the camera "bucket"---hell no. After a dive, rinse or not, I pat the lens dry with a clean microfiber towel and then keep it out of the sun if possible until back to the base where I rinse it in freshwater, again pat dry with microfiber and then allow to dry without the covers in place. If during transit from the dive site you need to put the covers on make sure there is no sand in them and that they are dry, remove them as soon as back to base and clean the lens.
There are some optical polishing cloths and compounds but those are best left for "experts" as a little bit is enough and a bit more then the lens is ruined.
BTW, the Inon lens is a coated lens, the coating is fairly durable but it is not beyond damage as you have found out. It is there to increase optical transmission and reduce glare and increase contrast.
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