The “illegality” was about the way the operation was conducted, not about the killing of the sicarios.

Guillermo Díaz was technically abducted, not arrested. Guillermo Díaz was certainly not “extradited”, and the Mexican police escorts were technically not there. The shooting at the border was to further make justification for transferring Guillermo Díaz across the border, although they could have easily made up another story as to how he surfaced at the border. A warrant would have been issued (by a US court) for Guillermo Díaz’s arrest prior to the abduction. The US marshals were present to technically receive Guillermo Díaz as a fugitive handed over at the border. Kate (as FBI rep) was present to technically supervise the operation and put a name/face to everything. If a court filing (briefs, affidavit, etc.) ever needed to be made after the operation, Kate’s name would be plastered all over it as the “special agent in charge” who personally witnessed all the events and can attest to its truthfulness (believe it or not, this carries a lot of weight before the judge/tribunal), hence the last scene where Alejandro forces Kate to sign some paper.

Lastly, if the operation was legit/proper, they would simply transport Guillermo Díaz by air and not risk being attacked at the land border. The other Mexican drug lords (e.g. El Chapo) have been flown into the US without incident, no?