"Grandfather has left the photographs at home."
Translation:Дедушка забыл фотографии дома.
I feel like this sentence/translation is a little misleading - but maybe not.
I thought забыть was "To Forget".
What if Grandfather left the photographs at home on purpose? Is there a verb for that?
Yes, забы́л can only be used if he forgot to take them. If he left them on purpose, you’d use оста́вил.
Why the variant "Дедушка забыл дома фотографии" is not right? There is no any difference in Russian where the object is.