For the record, yes, I've done it, and it's easy:
On the first floor, in the right end of the airport is a small office of Migraciones on the left side of the hallway. There was only one person in line ahead of me. I asked the women if she spoke English and she said no so I explained in my bad castellano that I needed to pay the fine. She asked me why and I gave an explanation, again in my bad castellano, paid her the ARS 300 fine, and was finished within 10 minutes.
Be sure to show the receipt to the guy who checks your passport later to avoid five uncomfortable minutes of him looking at the passport in confusion.