Bretton Woods wasn't about military protection. It was about stabilizing the global economy and monetary system. It absolutely gave the US a ton of economic influence, but it didn't have anything to do with military protection. The Soviet Union even took part in the negotiations that turned into the Bretton Woods Agreement, although they chose not to sign the treaty.
The US' military hegemony came out of NATO, the Cold War, and the Marshall Plan.
Well, we now know for a fact that Abrego Garcia is still alive.
And it's not about him lying. Of course a piece of shit like Bukele is more than willing to lie to anyone. The point is that he is benefitting politically from this arrangement and if he doesn't uphold his end he can suffer political harm. It's not just a promise, it's a two-way deal.