"It's curious that a group of presumably intelligent men would petition an official of a foreign power concerning a purely domestic situation. What was Seward supposed to do about it? Why wouldn't these men write a judge, a legislator, a congressman, or even the Confederate Secretary of State? If I had a problem with the IRS, why address my complaints to the British Home Secretary?"
Having not read the actual document, I am only guessing here, but consider this possiblity:
Why would they petition a government (CSA) they believed had no right to exist? Perhaps in pleading with Seward, they expected that, since we were still in that "gentlemanly phase" of the war, where many accepted rules were still being followed, he would be able to intercede with the Confederate gov't on their behalf. Or, on the other hand, they may have naively thought he could dispatch an army to ride to their rescue.