I've had this and fixed it
I had this problem on my MBA. I took the kit into an Apple Store and they diagnosed the display and defective and in need of replacement and this was priced at £600 sterling. I took it home, cried and began to work around the strip of interference while I decided whether to give this device a Viking funeral or get it done. Quite by chance I decided to clean the display with a cleaning wipe that I had bought from an Aldi store, made for cleaning spectacles. The screen came up like new but to my relief and amazement, the display went back to normal! Every few months is starts to go again, I wipe it with one of these wipes and it's fine again. The trouble I have now is that the strip has returned and I have run out of wipes! This is clearly (no pun intended) static so go down this route.
I ALSO registered just to say thanks. Your advice just saved me a load of hassle and money. I was really dreading having to fork over a few hundred dollars to someone to fix this annoying problem. huge relief. you've got some good karma coming your way buddy.