How to manage notice advance recovery amount ?

Hi! So I have resigned from my company as I am pivoting towards Law and joining Law School. My program starts in first week of July. However my contract states 90 days of notice period.

They have agreed to relieve me before my university joining date however they are asking for notice period advance recovery amount i.e equivalent gross salary for the days of notice period not served

I cannot move my date of joining as I have to join on campus by first week in July.

The Notice Period Recovery amount is a significant amount.

Also since I am pivoting in a new career, my hypothesis here is that I do not require experience or relieving letter

How do I navigate through this maze? Anyone who has experienced similar issues and can suggest ways to negotiate and go about it?

Thanks