Can a child have sickle cell trait if neither parent has it but the paternal grandfather does?

No: If neither the mother or father of that child carries the sickle gene, they can not pass it on to their own child to give them trait. In such a case, it stopped at the paternal grandparent. The sickle mutation is well known & thought to originate in Africa hundreds of years ago. Trait carriers suffered less with malaria. A new mutation , while possible, is rare to unknown in this disorder.

Mendelian?: If sickle cell is inherited in a classic mendelian pattern and a child carries the trait, then it was most likely passed down from a parent. If the parent does not have it then one of two possibilities: 1. de novo mutation 2. sickle cell trait is more complicated than simple mendelian inheritance pattern and if so, likely because more than a single mutation can cause the trait.

No: Both parents may need a repeat hemoglobin electrophoresis as it is likely that one of the biological parents have at least a sickle cell trait which is usually asymptomatic