With as much public fanfare as possible, send the first few planeloads to Afghanistan, Ukraine, and Haiti.
We have no obligation to return these invaders to their last suspected country.
Then broadcast the deportation lottery nightly. Make it a game show like "The Running Man", except the invaders face "The Wheel" of countries they're going to be deported to. Maybe they'll get lucky and even get deported to their home country. Who knows? Viewers can place their bets online.
The invaders will scramble to self-deport and capable countries will do whatever they can to stay off the list of Random Destination Countries by recalling their invaders. If we're running a "trade deficit" with your country, we're going to make that deficit up - just not with those you dumped on us. I hope the invaders we dump in your country aren't hardcore criminals but hey, you'll figure out what to do. After all, you had no qualms about dumping your invaders on us.
The globalists and their politician puppets around the world laughed as they dumped criminals into the United States. Now let's see the reverse.
I don’t think your idea will work and I suspect it isn’t legal. The deportees need to be returned to their jurisdictional countries only, any other countries will refuse to take them. We have to send them back to their own countries.