Kid Or Kit Gloves Expression. I would imagine the kit gloves reference was just a typo. They date from the 18th century though early ones were often made from the more available lambskin.

If you treat someone or something with kid gloves or if you give them the kid glove. Is the phrase handle with kit gloves or handle with kid gloves. I would imagine the kit gloves reference was just a typo.
Definitions by the largest idiom dictionary.
The expression is kid gloves. The phrase comes from the early 1800s where a physical glove was made from young lamb or goat s skin and had a very fine soft touch to them as opposed to other gloves that were made from strong leathers. Kid gloves were made from the skin of a young goat or lamb which is much softer than gloves made from other leather. What does handle with kid gloves expression mean.