I am thinking by the picture you still have a lens in front of the diode and the contaminate is on the lens. If the lens is in place and you turn it the artifact with rotate with the lens. If it is on the diode window it will remain fixed. I am thinking as well if it was on the diode window it would have already burnt. If you have the means to run the laser at a very low current just over lasing threshold I strongly recommend doing that before powering it to full again.
It is likely burned into the window. If that is the case, you might want to leave it as your only alternative would be to decan the diode. That could seriously reduce the life of that diode.
This guy's video go against just about everything that experienced members have posted.
Not any kind of alcohol like he say's, it matter's. Recommened 99%+ pure and a bike pump has to much moisture..
decan is the best method I though. but I will be risk because the dusk can get touch the laser diode chip. I've done some window cracking and 1 of laser survived (My 515nm T-DRAGON build).