A grackle shouldn’t be able to reach nestlings. Is the entrance hole 1.5″ in diameter? How far from the bottom of the hole to the bottom of the box? That measurement would be important also. Are there seed feeders near the nestbox? They shouldn’t be anywhere nearby if you have birds like grackles around. Just like everybody else, they defend food sources.
Wire predator guards would give any harassing bird a good place to perch. I wouldn’t use one. I would make sure the entrance hole is the proper size for starters. That should keep big shoulders out and the nestlings out of reach if the next isn’t high in the box.
Have they actually robbed a nest in your box?
Gin
Atlanta, GA