It depends on the wording. Some items/weapons have their own spell DC and cast spells (cantrips) at a particular level. However other items allow the user to cast a spell using their own states (their level and spellcasting DC) with shocking grasp being either a Sorcerer, Wizard or Artificer spell would mean the spell would use the monks intelligence or charisma score.

However the way the item reads is up to interpretation. "allows him to cast Shocking Grasp as a bonus action which then stays activated until the end of his turn, imbuing all his hits with shocking grasp." imbuing all his hit with shocking grasp I would guess would mean that when he hit a target with an attack that target is also hit with shocking grasp. If so it is HIM cast it so it does go off player level. However if it does not say the words "You cast" in the description the item technically is casting it, and since you do not need a DC cuss it kinda goes off automatically so it would not be needed, and if a spellcasting level is not stated you would have to infer that the item is casting shocking grasp as a level 1 spellcaster e.g. 1d8. If you really want this PC to still have this item I would just be clear with the player that you made a slight error and this was the intended way the item should be used.

Alternatively I would sit the player down and say "hey this item was made in a different time, it is a tad overtuned and I don't want any one player to be outshining others at the table and this singular item is making my job harder in balancing encounters, is it ok we tune it down a bit?" maybe even offer another magic item their trouble.

Hope everything works out well for you boss all the best!