Interestingly enough, t
he Bush-era State Department brief on the Logan Act basically agrees with a similar 1975 State briefing that, based on the history of the act and established case law, members of Congress are perfectly enabled to meet with foreign governments as long as they do not intervene in disputes between the US and those governments (i.e. directly contravene or counter offers made by the executive branch) and the reasons why they are going fall within their legislative responsibilities.
I.e., as Speaker of House at the time (3rd in line of succession), Pelosi was perfectly allowed to meet with Assad to learn what his points of view were as they pertained to the United States. It was, IMHO, a stupid, incredibly partisan move that she deserved to be criticized for, but unless there is evidence that she actually interfered with terms of negotiation, she is considered to be in the clear. Repubs at the time liked saying that she had interfered, as the Bush administration had counseled her to not go, but at the same time the Iraq Study group and the State Department actually recommended that legislators do learning trips overseas. Which again, makes it partisan, but not really interfering.
The brief concludes that, as worded, since the basis upon which US negotiations are actually undermined is determined by the State Department and can only be directly prosecuted by the Justice Department, both of those departments need to agree that the Logan Act was violated to realistically prosecute. Ted Kennedy, according to the brief, actually tried to get the Act repealed because the vague wording made it more of a political tool than a real law, but he got talked out of it.
In this particular case, it would be hard to argue that the letter was
NOT intended to directly interfere with negotiations, as it pretty much says that in plain English. However, Zarif himself has basically laughed off the letter as nonsensical, so it hasn't really interfered in the terms of the negotiations besides making the US look like a laughingstock. So I suspect that regardless of the any number of petitions, the DoS and DoJ will basically ignore this, because there is no point and actually indicting anyone under the Act (which has never ever happened) would open up a can of worms.