And, more recently, Bukele and Trump insisted that they would not return a "terrorist" to the United States: https://bsky.app/profile/atrupar.com/post/3lmrwrrkbnf2e
It's clear that the administration does not consider collateral damage a bug, but a feature; it confirms that as long as they insist that they will not do anything, then nothing will be done.
This phrasing buys into the Trump admin's narrative.
They did not determine that it was impossible to get him back. They have chosen to not pursue it. They refuse to define the agreement between the US and El Salvador sufficiently for anyone to know what is or is not possible through that path. They also seem to refuse to use political or financial influence to go beyond whatever that agreement may define.