Once they are there thats a problem they can and might stay inside the figs. Not sure maybe hose them or something off tree but you wont get the ones inside the figs already.

The best way is to prevent them in first place and i find the a product called Tanglefoot works excellent, its a waxy like sticky substance that one puts above soil line on the trunk. Some put tape on tree and then smear it on the tape there are various ways to apply it in this fashion.
Its all natural and has 4 ingredients very simple but crawling only bugs cannot pass it. I had same problem years back and its heartbreaking when one first finds this problem, but no more ants in figs for me now.
Next season if you try it will work very well im sure .
Martin

They seem to go for the ripest figs. If I picked the fig slightly before it's fully ripe, will it ripen off the vine to be sweet?

No they will not.

Thanks dieseler.

THISISME has seen a few ants too.

frd:
Welcome to the Duke City. You have several fig-growing friends living here. Contact me off the forum anytime.
Leon

I dropped my figs in a pail of water as I picked them and almost all the ants died and floated to the top. There were a few left but it was easy enough to pick them off as I saw them crawling around. Then I pulled them apart to check for more ants, but didn't find many. I kept an eye on them for a little while to inspect for more ants, but to tell you the truth, the figs are so delicious at that stage of ripeness, I don't mind if I happen to eat an ant or two that failed to crawl out of the fig. Of course, when I start picking them in greater quantities, I can see how it will be a problem. But dropping them in water takes care of the majority of them. I suppose if you let them stay in the water long enough they will all eventually drown. I didn't wait very long, because I was waiting for my breakfast figs! And no, the figs did not get soggy from being in the water.