I have quite a lot of hours researching British India. Both military and a steam locomotive driver from County Durham who emigrated there in around 1890. There is no evidence on any ecclesiatical record of a Peter or Catherine Pickett in India, second half of 1800's. This would include the the dominant religions, Catholic. CofE and Methodists, etc.. They operated with the certificate, or a quarterly listings system just like in the Mother Country. Variants are Piggot and Pigot. Check on familysearch.org