[Tell It Right]

Take them to the nearest embassy/consulate of their home countries and dump them there. Let the home country pay to take them back.

Assign border security guards at the embassy to confirm they don't leave the embassy unless it's getting on transportation to take them home. And even travel with them if necessary.

Costly up front? Yes. But it puts part of the financial pain back onto the home countries that exported them here -- dis-incentivizing repeat occurrences.

[DIRTYSECRET]

Sounds good to me.