Welcome, and thanks for showing your family treasure. Here's how to tell if your grips are ivory, bone, or plastic.
Do the Hot Pin Test (from
http://www.wikihow.com/Tell-Ivory-from-Bone )
1
Heat a straight pin. Hold it over a candle flame or a lighter flame for a few seconds until it gets quite hot. You can use any piece of metal, but a pin is a good choice since you don't want to create a mark on the item you're testing.
2
Hold the pin to the surface of the item. Choose a discreet spot so you don't end up leaving a mark or a dent (although if the item is ivory, this won't happen).
3
Smell the place where you touched the item with the hot pin. If the item is ivory, it should have no scent that wasn't there before. If it's bone, it will smell faintly of burning hair.
True ivory will not get damaged by this experiment, since it is hard and strong enough to resist the heat. However, if the object you're testing happens to be made of plastic, the hot needle will make a slight dent. Since some plastics (such as Bakelite) have as much or more value than ivory, you may not want to try the hot needle test until you know for sure that what you have is not plastic.