This seems to be common with wrasses and often happens out of nowhere. You're lucky it doesn't have a spinal injury and seems to be just a mouth injury. Obviously keep an eye out for lethargy and weird swimming. If you see that, it's almost certain it will starve to death.
I don't really think you can do anything that wouldn't cause more harm than good. I think the only advice I've ever seen is QT with Epsom Salts added to the water. Removal would probably be worse than nothing, especially since the Epsom Salt treatment seems to have a success rate of precisely zero.