Are you sure you ordered a hanna nitrate checker? Because like Randy says, I don't think they sell a nitrate checker for salt water. Perhaps its a new product, perhaps I am being a numpty, but I can't find a pocket checker for nitrate on their site. There are several nitrite checkers, but thats not the same thing (nitrite vs nitrate).
Re your high nitrates, since you also have phosphate present, you would seem to have enough to feed plants or bacteria. Are you only using algae to remove nutrients? I've not used algae successfully myself to reduce nutrients before so don't really know what the true potential for that method is, but I can say that carbon dosing like vinegar or vodka would probably work well for you in this situation. Randy uses both algae and carbon so they can be used in tandem.