Which airport? You could call the specific airport you fly into and check to see if they have special screening for that and what it entails?
From what I can tell, the ones that consider themselves Zika gateways are doing their best to educate people. No active screening except they're on the lookout for symptoms. If they see symptoms in legal travelers, they refer those people to secondary screening and the CDC. I found one article that said that if they see illegal immigrants with symptoms they will quarantine those from the healthy illegal immigrants. Who knows why.
But the gist I found was that CDC doesn't recommend special screening because it doesn't do much good. Most people who contract the virus don't show any symptoms at all. Additionally all of the travel warnings focus on pregnancy and sexual transmission. Basically, wear mosquito repellent and make your partner wear a condom during sex.
There have been visa issues due to the recent politics and that's shown up in the news a lot. But it's not linked to disease that I can tell. And honestly, anything that could affect re-entry could also affect your status if you did not travel. The political scrutiny is supposedly aimed at preventing fraud but who knows.