I wouldn’t be surprised if their legal theory is that they will win the rights to Mangione’s likeness in a future civil suit. If a judge is willing to claim to believe that, then I could see an injunction being issued.
Does that sound ridiculous? Sure, but we’ve seen some absolutely crazy stretching of the law these past few years.
IIRC a landmark trial in early post-WW2 years resulted in it being impossible for third party to own complete rights for someone's natural likeness or other natural features (like voice, which was specific case involved).
So they can't win the right to prevent distribution, they can win the right to use the likeliness, but for distribution they would need to have active contract with Mangione that they are representing him for that, which I somehow doubt being the case.
Does that sound ridiculous? Sure, but we’ve seen some absolutely crazy stretching of the law these past few years.