When this was still the United States of America, The President and Secretary of State, would recognize there responsibility to protect it’s citizens.
They would use flowery language to send a quiet message to Mexico and tell them, “send our guy home now, or, we’ll come and get him.”
There would be a quiet response from Mexico, to the effect, “Sorry for the misunderstanding! Do you think he would like a beer for the road?”
Back in the early 70’s the Marines at camp Pendleton did just that after one of their Men was locked up on a bogus charge in TJ, they went down there 300 strong FULLY ARMED and removed him from their jail and brought him back home, and there was not even a peep from the Meican Government or any Government Official from either side of the tortilla.