Lying aside, this is setting up a really weird question regarding sovereignty. It represents just another way that modern conceptions of sovereignty are becoming less and less territorially bound.
Another example, which also sheds light on why this is such a strange claim from El Salvador, would be the enforcement of laws in border zones. Under older conceptions of sovereignty US agents can enforce US law on US soil, and the same was true for its neighbors. However, more recently the law changed such that we have bilateral agreements with our neighbors that allow their agents to enforce our law on our soil, and vice versa, within 100 miles of the border. From the classic conception of sovereignty this makes no sense, other than that the nation’s law is still territorially bound.
The case here with El Salvador is even more interesting. El Salvador is saying these men are locked up under US law in CECOT, and that they are the responsibility of the US. Which means that now the law of the US is not territorially bound, and is being implemented in El Salvador over these men. It’s hard to convey to someone that hasn’t studied sovereignty academically just how absolutely bonkers that is.
For a similar but contrasting situation, think of immigration. If a country wants to remove migrants it doesnt tell the country they came from to come in and get them. Removal is a legal process carried out by the state, under its law, as an exercise of sovereign control over its specific territory. Asking agents of the other country’s government, who have no legal jurisdiction to do anything, to come and get migrants would make no sense.
El Salvador here is basically ceding their sovereign control over these specific people despite the fact that they are obviously in El Salvador, and therefore are subject to Salvadoran sovereignty. This isnt something that any country has ever done, except with regards to very specific people like ambassadors, or very specific spaces like embassies or military bases