Is it true the drone has a grandfather but no father?
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 had 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.
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 sex is based on the number of chromosomes they receive. So the use of the term “grandfather” in this context is kind of a stretch, but if helps you understand, go for it.