What is the term for a 25-string fretless lute that features a skin head stretched over a gourd-shaped
body?

Sarod is the term for a 25-string fretless lute that features a skin head stretched over a gourd-shaped body. It is used mainly in Indian classical music. 
A Sarod is a 17 to 25-stringed lute-like instrument of India. It has 4 to 5 main strings for playing the melody, 1 or 2 drone strings, 2 chikari strings, and 9 to 11 sympathetic strings.

Ithink that c would make the most amount of sense.