Find the source of the problem. Mosquitoes usually like stagnant water, but since your system is recirculating they are coming from somewhere. If you find a source you can eliminate that would help get rid of your problem (i.e., standing water from flower pots, buckets, barrels, tires, tarps, pet dishes, bird baths, swings, wading pools  anything that collects).
If it was my system, I would clean it out  I would be concerned about eggs.
Make sure you have good ventilation  carbon dioxide attracts mosquitoes. A fan might chase them away but you still need to get rid of them.
Use screens to keep them out of your growing area. I installed a fine mesh screen to keep mosquitoes out of mine.
Protect yourself until you solve the problem  long sleeves, pants, and avoiding peak biting hours.
I firmly believe in mosquito control. I empty my pots with containers below them daily & let them drain. I also keep my gutters clean & use flying insect (bottle) traps. I try & do my last lawn watering in the afternoon so it burns off by night.

The use of larvacides, bug zappers, & insecticides changes as more information is found. Some sites that update their information are NIOSH, the CDC, & EPA.

Here is a mosquito site:
http://www.mosquito.org/info.php

Baci,
Thanks. I am guilty. I need to stay on top of it better.

You can put a couple of drops of pyrethrins in your nutrient tank or a Mosquito Dunk from a garden center. Mosquito dunks are BT-Israelensis a fairly low-toxicity safe product.

The mosquitoes growing in my tank ends up as betta food. :-)