A comparison of the fragmentation produced by the detonation of a Type 97 hand grenade and a British No. 36M is is below. Both are cast iron bodied grenades with external grooves. The image is taken from the 1945 C.I.AMN report 'JATR-No 05 - Discharger, HE, Type 91 and Grenade, Hand, HE, Type 97'.
As can been seen the grooves do not, in general, control the fragmentation process to any real degree. Though the grooves will act as stress risers, they should be on the inside surface to control the body's fragmentation. For maximal effect the grooves should be far smaller and the casing thinner, though using standard cast iron with such a design may be problematic.
A thinner casing and body internal surface patterning (preferably on the top, bottom and sides) would result in more numerous and higher velocity fragments of a controlled weight. Though lighter, the higher velocity and greater number of fragments means such a grenade would be far more lethal. It would also minimise the highly dangerous larger longer-ranging fragments that both of the earlier design grenades produce.