You could put it that way. The drone arose from an unfertilized egg and so he has one set of chromosomes from the queen (his mother) and no father.
But his mother arose from a fertilized egg. That means she has two sets of chromosomes, one from her mother and one from her father. Since she had a mother and father, her son (the drone we are talking about) could be said to have a grandmother and a grandfather from her side of the family. He has no other side of the family because he has no father.
You as a human have two grandparents on each side of your family, so you have two grandmothers and two grandfathers. But a drone has just one grandmother and one grandfather. So the drone has one set of grandparents on his mother’s side of the family and no father.
So although the drone has a grandfather but no father, the grandfather is on his mother’s side of the family: the drone has a maternal grandfather (and grandmother) only.
These terms are more apt for animals that arise from normal sexual reproduction where each individual has two sets of chromosomes. Bees, along with many other insects, are haplodiploid, meaning their sex is based on the number of chromosomes they receive: females have two sets and males have one set.
In short, the relationship words in this context are kind of a stretch, but if helps you understand, why not?
Honey Bee Suite
This quote, about male bees having no father, only a grandfather, I use all the time when teaching about bees. I share it especially when showing the insides of a mason bee tunnel, where it is pretty easy to see the cocoons change size from female (back) to male (front). The quote is a great way to get folk to stop and think (and remember) about how reproduction for bees, (wasps, ants) is very unlike us humans.
Do male honey bees have mother-in-law?
Drone is a diploid offspring. It has two sets of chromosomes. So the answer is wrong. Right answer is sterile female (nurse) which is produced by unfertilized haploid egg. This sterile female female is a mongoloid individual which has no father.
You have it exactly backwards. Haplodiploidy is a sex-determination system in which males develop from unfertilized eggs and are haploid, and females develop from fertilized eggs and are diploid. Look it up anywhere.