What’s the proper way to correct someone when not saluting an officer?

It is not aggressive attitude. An enlisted service member is required by the UCMJ to salute an officer. If not in a combat zone.

I'll take a page from my friend "J" the Marine Major. Funniest "No s**t, there I was..." story I've ever heard.
Offutt AFB - two junior enlisted Airmen come out of the BX/PX complex and on the ~20 yard walk to the asphalt, pass then Capt J. They saw his rank and intentionally looked at their shoes as they passed. He whipped around and yelled, "HEY! ARE YOU GONNA JUST EYE-FUCK ME OR RENDER THE PROPER COURTESIES??" lol
The second half of the story is even funnier.

There is no better way. You were right.

There is no better way.

My preferred method was to render the salute with a hearty greeting. As others have said, the junior person may have been distracted and didn't see you.

Your were right don't worry about it.

Ok I gotta reply to this one. Some back ground here I was in AFJrRotc in high school for 3 years, my stepdad was all about VMI and I had been in the Army for well over a year. So I knew military protocol. I got a severe concussion and had been completely unconscious for 30 minutes or longer, over night at Frankfurt Hospital and had half my uniform stolen while in the hospital. My hat, hair bands, and hair clip were all gone. I had no hair brush or even a rubber band to make myself presentable. I asked for those things and was told to stuff it by hospital personnel. As I exited the HOSPITAL looking like something the cat dragged in and unable to remember my name much less my protocols. I passed 2 officers who I didn't salute and got screamed at for 20 minutes over not saluting them. I was sick, confused, couldn't focus, or see and generally was bewildered at their anger over my failure to salute. Not having a PROPER uniform and Why my hair (Waist Length) was not in military regs. I had lost more than 6 months totally, a year of my basic training, and all my ROTC training in one fell smack. I still only remember pieces of my High school and not much of my first year in the military. I apologized profusely and saluted. I vaguely remember hearing my 1st sgt , who had come to take me back to my unit, behind me explaining to them my situation but no one came to me and apologized or said hey are you ok? Not saying that was her situation but it was mine. Sometimes there is a reason...……..jus' sayin'

There is not enough info here. We cannot tell the tone of voice or other factors; that being said failing to salute an officer can result in administrative punishment under the UCMJ should either officer want to pursue it. Most likely an on the spot correction was all that was needed but at the same time the MAJ coming down on the LT in front and enlisted Soldier is not acceptable in any circumstance. That is a conversation for a private area.

I remember a number of years back, a group of warrants and I were trailing a 2nd Lieutenant to the chow hall when he crossed paths with an enlisted Ranger who didn't salute him. The Lieutenant about faced and yelled after the ranger "Do you see this!!" Pointing at the rank on his cover. The ranger shot back, "Do you see this!" Pointing at his ranger beret and kept on walking. The Lieutenant was speechless and dejected, we took him into our gaggle and protected him through dinner.

THE QUESTION IN POINT IS THE ONLY WAY TO BE ASKED.