"Grandfather has left the photographs at home."
Translation:Дедушка забыл фотографии дома.
Yes, забы́л can only be used if he forgot to take them. If he left them on purpose, you’d use оста́вил.
Ah, yes, that makes sense - but in this example it wouldn't really change the meaning of what is being said: he left the photos at home or in the house - it's basically the same, isn't it? One could argue that 'in the house' could be not his but someone else's house, but then the same could be said about 'at home'.