I see now.

Admittedpy, there are very few intimate enough with summoning rituals to modify them without disrupting it's original function. Notable exceptions are the Einzbern, who created the system, and Lord El-Melloi who was a prodigy. 

If you want your character to.have this sort of background I'd suggest the following:

A) Flesh out the Mentor with a backstory and history in magecraft so I might use him/her as an NPC. Notably their involvement in summoning and how they became so proficient.

B) Have your character be accidentally granted the servant through a miscalculation in the summoning rituals that makes Li the true master much to her mentors dismay. This would add an air of danger and tension betweenthe two of you.