I would assume that a court of competent jurisdiction refers to the federal, state or local court having jurisdiction over the place where your grandfather died or at least the place where his death certificate was filed.
But if you don't know where he died, that doesn't help much.
Or maybe a court in your home city can be considered to have jurisdiction in your case, since you are trying to obtain records of a family member, no matter where those records may be found. You may want to contact an attorney (which means $$) to see what options there may be. I'm not a lawyer so I'm out of my depth here.
Will the Coast Guard give you any hints, like the most recent record of where he lived or on which ship he served and when, which may hint at his location near the end of his life?