Dogs can and do sometimes chew up and eat homework.
However dogs do not specifically eat homework.
The excuse of dogs eating homework has been going around for years when kids and students didn't want to or did not do their homework.
So the student would tell their teacher that the dog ate their homework which would be a reason why they did not do their homework.
That then just ends up with the student being given more homework to do.
I used to tell my teacher my dog ate my homework and I always got more homework to do.
Dogs do like to chew up paper and so if you left your homework where the dog had access to the homework then it could be possible for the dog to chew the homework up.