Which award may be granted for entering any inter-service competition?

The Inter-Service Competition award is specifically designed to recognize and honor the achievements of NJROTC cadets who participate in competitions against other branches of the military. This award acknowledges not only the effort put into training and competing but also the spirit of camaraderie and teamwork fostered through these inter-service events.

The other awards listed serve different purposes: the Color Guard award acknowledges proficiency in ceremonial duties, the Leadership Training award focuses on leadership development, and the Marksmanship award recognizes shooting skills. None of these awards are universally granted for participating in inter-service competitions, making the Inter-Service Competition award the correct choice for this question.