If this is a vein then there are several options for treatment including removal through a microincision, sclerotherapy, laser, micro needle radiofrequency or ohmic thermolysis. It is difficult to tell from the photo what the hard area is and this would be unusual to be a vein. You should see a vein specialist who can answer your questions, make the diagnosis and determine if fraxel if right for you.
Varicose Veins of the Eye
Interesting that you ask - in a couple of days you will see a video clip uploaded to my website from a segment on the Doctors TV Show where a vein specialist (Dr Raffy Karamanoukian - my brother) showed how he does this procedure on a patient. You can contact Dr Raffy through his RealSelf page or go to his website at SantaMonicaVeinCenter.com