looks like hair algae. easiest way to get rid of it without adding something that eats it is to take the plant out and dip it in a 1/5 solution of flourish excel for 30 seconds, or you can nuke it in the tank with targeted applications.
a total blackout could kill it, but it takes a while to die, so you may end up killing your plants. reducing to photoperiod to no more than three hours on with an hour or two of darkness before turning them back on can slow it down in the mean time. its not an easy algae to get rid of, but it isnt impossible.
Yup, probably hair algae. I would personally recommend picking up a bottle of Flourish Excel and a syringe, and using the "target" method. Turn off your filter and squirt the excel right on top of where the algae is (a small amount goes a long way). Let it sit for about 10 minutes or so, then turn your filter back on. You should notice that the algae turns red or white after 24-48 hours, which is a good sign that it is on it's way out. If you don't notice any color change within a couple of days, repeat the treatment.