Hi Anamika. I don't know if I have any suggestions for a 'green gift' for grandmothers in particular. I just go along with the usual green ideas for our environment: less paper, recycling, etc.
We recycle our paper, plastic, glass and aluminum. I recycle any plastic bags I get back to the store or other places, (i.e. library) who may need them for patrons books.
I'm a real 'bag' lady. I love the canvas bags and there are a 'ton' out there to choose from. Love the ones with the multipockets. Helps when I go to work (nurse) or carry my writing to the library.
Hope this helps.