Search online for information regarding the British Indian Army. They were commanded by British Army Officers. I read that they were, however, expected to learn to speak the Indian languages of their men.
You may be able to obtain your great grandfathers military records. More here
The date engraved suggests that it is a commemorative item based perhaps upon a cap badge. As referenced by @Johnny_Anonie many Indian regiments had British or Anglo-British Officers during both the Great War and the Second World War. The Wiki link you provided in another thread indicated that your grandfather served in India.
Obviously the devices on the badge are those of the Republic of India because it is dated 1973. It is possible that prior to the Indian Independence Act of 1947 the regiment's insignia carried the British crown. The item may have been given to your grandfather by the regiment as a memento of his previous service. Your grandmother might know more.
Funnily enough my own grandfather served on the North-West Frontier of India with the Indian Defence Force during the Great War. My grandfather was born in India in the 1870s after his family emigrated from Ireland.
He spoke several Indian languages fluently. He was very insistent that it was uncouth to eat a curried meal in the evening. Breakfast and lunch only!