Notice Period and Early release from the company on completion of ongoing work

Hi, I am currently employed in an MNC and working at client location. I am on notice period for the last 1.5 months. I am working with this same company for the last 7+ years and on the same role - having been denied promotions despite multiple client recommendations. And this was basis enough for me to decide to quit the company. The offer letter I have signed with the company has the below clause on notice-period: "During the probation period, if your performance is found to be unsatisfactory or if it does not meet the prescribed criteria, your training / employment can be terminated by the Company with one month notice or salary thereof. On confirmation as a regular employee, you will be required to give three month’s notice or salary thereof in case you decide to leave our services. In the event of you having any incomplete assignment, the Company will have the discretion to relieve you only at the end of the three month’s notice period. Similarly, the Company can terminate your services by giving you three month’s notice or salary thereof. The Company may terminate your services immediately on disciplinary grounds." I have completed my assignment along with that the hand-over of any pending activities to my replacement. The client I am working with has acknowledged the same and released me from the project. My understanding of notice-period is - if the assignment has been completed, then the company should not have any issue in releasing me from the company. But, my reporting manager at offshore is asking me to come back and serve the notice period there, indicating I would be assigned new work. I have enquired with the HR on the buy-out option, and they say it's not in the company policies. I seek your advice on the below: 1. Even after my work is over, am I expected to take up new work during my notice period - do I have the right to deny that? Taking up new work, per my understanding, defeats the purpose of notice-period, and I don't intend to do this. 2. Is it right to deny the employees to even keep the buy-out option when it's been proven that the work has been completed and the client has acknowledged the same? 3. My understanding of the term "assignment" in my offer letter is ongoing work with the company. But, the company seems to take it that I could be assigned to any other work in the company. I haven't seen any documentation on this as such though - only "clarification" that the HR has provided. Is there a way to challenge this understanding? Thanks in advance.