Aircraft tug driver reported a B737 Max was being repositioned when the TTWS went off. The tug driver stopped the tow and noticed that the aircraft's nose gear had shifted excessively in the tug cradle. Tug driver recaptured the nose gear and continued the tow.

Narrative

Today; I was assigned to reposition an aircraft. I was assigned to Super Tug X; a TBL 50; it is a smaller tug. Previously we had only used these tugs to reposition regional jets. But recently the company decided with could use them again to reposition a 737 if the weather was dry and no wind. I was pushing a 737 MAX; Aircraft X back from Spot XX onto taxi lane XX for a west tow. About half way across the taxi lane; the TTWS System went off. I immediately stopped the tug and aircraft. A deicer truck had gotten close the aircraft. This is NOT why I am submitting this report. The reason I am submitting this report is because after I stopped the tug and aircraft; I could see that the nose gear of the aircraft had shifted within the tug cradle and when I stopped; because the MAX sits higher and I believe is larger than other 737 it pulled the cradle out of the tug an alarming distance. I was concerned! I alerted the Observer that we had to go back to Spot XX and told the Tower. I pulled the aircraft back in without incident. the aircraft was chocked and lowered to the ground. My Supervisor came out to check things out and said I over reacted; to someone who does not move aircraft the position of the nose gear inside the cradle may have looked normal; but I knew how it appeared when I first captured it and was not happy with how it looked now. Although the Supervisor said I over reacted; I recaptured the aircraft nose gear and proceeded to reposition the aircraft without incident but concerned about possible issues in the future using this small tug moving 737 MAX aircraft.