Dear Manuel,

Sorry for the delay in getting back to you.  This is a valid question.

The Church does not, to my knowledge, have a teaching on this. I do know that yoga has been associated with demonic possession, but taekwondo is not yoga. Still, it's association with eastern pagan religion gives one pause, and the demonic is a reality, even when one is not explicitly aware of participating in it.

You are right to avoid any and all spiritual elements to the practice. My research has been unable to identify a specific meaning to the two-headed dog. I guess you have to evaluate the positive affects you get out of taekwondo against the spiritual hazards.