You have to cut the lateral line out of the filet. The lateral line is more sensory organ than meat. AKA the blood line or mud line, it's the oily reddish stripe running down the filet. That is the where the strong flavor comes from. Other species (like stripers or catfish) also improve in flavor if the blood line is trimmed from the filet but with common carp removing it is pretty much mandatory. A brief soak in salted water or milk will pull out some more fishyness.
Even so, it's still a bit fishy; perhaps more so than most Americans like to eat. The rest of the world loves the stuff. Don't saute up a simple filet like it was Dover sole or halibut; it needs something more than lemon and butter (unless you like a strong flavored fish like mackerel). It works best with traditional Asian and African recipes like curries, braises and spicy fish stews. Carp has been on the menu there for millennia. Pair it with strong flavors like ginger, garlic, shallots, spices, curries, chilies, fermented bean pastes, shaoxing wine, etc.. If you'll eat farm raised tilapia or catfish, then you probably won't balk at the flavor of properly filleted carp. Of course, the quality of the water is reflected in the quality of the meat. Carp feeding in muddy, algae slime water are going to taste crappy. Carp from clean rivers and lakes are what you want. I've read that bighead and silver carp are better (i.e. less fishy) for the table than the common carp but that common carp is much better than the lowly mud carp most often eaten in Asia. I have only tried common carp.
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