Do I need to dump my pumped milk during my biz trip to India? If not how do I keep milk in hotel and transit in plane?

It would be a waste to dump all away. If you are staying in a hotel, you can asked the staff to assist you by putting them in the freezer. When you are in the plane, you can ask the stewardess/steward to put it in the chiller so that when you touched down, if your family is coming to pick you, you can then ask them to bring a cooler bag together with an ice pack to transport it back home.