Jason,
Its tough to say from the pic what exactly the problem is with your colt, other than it is stressed by something. Your description of mucus indicates at least this much obviously... but does the animal have a necrotic infection? We cannot say from here.
You mentioned moving the coral (arghhh - avoid always when possible. Plan long and put a coral in thew best place the first time and allow room for it to grow... rather than crowding a tank with frags early on as is common. Perhaps the case here? A move away from another coral?) and you state that you did not change the lighting... yet that seems impossible. The move, even if linear, places the coral under a different position under the lamps (closer or farther away from the most intense place under the given lamp scheme center of the fluorescent lamps... inner circle of halide punch, etc). I also see in your pic that the colt is sitting on the sand bottom. Was the previous place on the sand... or did this critter take a downward move from the rocks?
None of the above is necessarily bad or fatal... but they are sources of stress (perhaps slight damage in handling that invites infection).
And as TippyToex has stated... we need much more information here to help you.
As to taling it out of the tank - no, please resist moving this coral at all if possible. Moving any stressed coral is a sure way to make a mater worse (often killing the coral).
best of luck,
Anthony