The dog pictured above was at or near the the Vietnam Memorial Wall, not the WWII Memorial.
My dad was a WWII vet and I’m a Nam vet. We had a dog the whole time I was growing up and I’ve had dogs all my life. My dad, who served in Patton’s Third Army, loved dogs.
I’m sincerely sorry about your grandfather’s fear of dogs, although in my experiences with many fellow veterans, I’ve never known one to express such fear. I would imagine it’s less likely among veterans than it is among the general population.
Like I said, my grandmother told us it was due to the war.