Impersonation of a foreign official.
Because ICC is not recognized as a court, if any officer of ICC claims to be be an officer of a court, they may be guilty of 18 U.S.C. § 915 impersonating an official of a foreign government.
, with intent to defraud within the United States, (likely made meaningless by guidance to 912) falsely assumes or pretends to be an ... official of a foreign government duly accredited as such to the United States and acts as such, ..., shall be fined under this title or imprisoned not more than ten years, or both.
In the DOJ guidance on what constitutes "18 U.S.C. § 912 personation of officer or employee of the United States", it states that "Government officials are impersonated by any persons who assume to act in the pretended character. Thus action alone may amount to a false pretense of federal authority. (by inquiring about passports, defendants pretended to be federal immigration officers)."
It is true that this is the standard for what constitutes "personation of a federal employee". However, "personation of an official of a foreign government" and "personation of a federal employee" are both parts of 18 USC part I chapter 43. In the absence of a more specific guidance for 915 (changing the guidance for 912), it is plausible to assume that the same standard, for what constitutes personation, applies for the purposes of 915 as does for the purposes of 912.
The reason for removing "intent to defraud" from 912 is that US v. Lepowitch "renders them meaningless".
Lepowitch, ... held that "intent to defraud" did "not require more than the defendant had, by artifice and deceit, sought to cause the deceived person to follow some course he would not have pursued but for the deceitful conduct."
Again, since the language in the 1st part of 915 is the same as it is in 912, it is highly likely that Lepowitch would apply in the same way to "intent to defraud" clause of 915 as it does to the "intent to defraud" clause of 912. Which is to say, Lepowitch would "render it meaningless."
The above-quoted part of Lepowitch actually addresses some of the objections which have been voiced in the comments to this answer and to some of the other answers to this question. It clearly states that the intent of the code is to make it illegal for people to use a ruse to make themselves appear to have more authority than they actually have. Such a ruse is illegal even if the ruse attempts simply imply (but do not directly assert) a position of authority.
American Service-Members' Protection Act
American Service-Members' Protection Act treats, and specifically targets, ICC as something slightly short of a terrorist group. It makes the precise legal standing of ICC akin to that of a vigilante group which has gained support of some foreign governments. The US tolerates ICC's seeming vigilantism as long as ICC does not attempt to impose its will on the US or US allies.
ASPA authorizes the U.S. President to use "all means necessary and appropriate to bring about the release of any U.S. or allied personnel being detained or imprisoned by, on behalf of, or at the request of the International Criminal Court."
"All means necessary" here is not limited to just political or legal means. This is how declarations of war are worded. "All means" includes all military means. Should ICC attempt to arrest any US military personal, it would be treated as an entity at war with The United States. At that point, rules of war rather than rules of law would apply.
The act prohibits federal, state and local governments and agencies (including courts and law enforcement agencies) from assisting the court. For example, it prohibits the extradition of any person from the U.S. to the Court; it prohibits the transfer of classified national security information and law enforcement information to the court.
This last part puts ICC on a lesser footing than a bouncer at a bar.
TREASON, SEDITION, AND SUBVERSIVE ACTIVITIES. 18 USC 2387
(a) Whoever, with intent to interfere with, impair, or influence the loyalty, morale, or discipline of the military or naval forces of the United States:
(1) advises, counsels, urges, or in any manner causes or attempts to cause insubordination, disloyalty, mutiny, or refusal of duty by any member of the military or naval forces of the United States; ...
Shall be fined under this title or imprisoned not more than ten years, or both, and shall be ineligible for employment by the United States or any department or agency thereof, for the five years next following his conviction.
If a foreign official attempts to contact any service member with intent to investigate that service member's or another service member's conduct, while that official is on the territory of the US, the foreign official may be seen to be attempting to cause disloyalty or refusal of future duty. This would fall under 18 USC 2387. This is a criminal offense.