I would not use neosporin, the tail heals naturally and the tail regens naturally, neosporin could cause the tail to stop the regen process by closing the tip of the tail too soon and not allow it to regenerate.
Yea the kid next door to me got a gecko a month ago and dropped a hid on the end of her tail. A centimeter came off then later that night she dropped the whole thing. I feel bad for him, but he should of not dropped the hide on her. People make mistakes. Then he got on my comp when I was at the reptile expo.