User blog comment:Underscorre/Jeff the Killer Rewrite Contest!/@comment-5973399-20151003202655/@comment-25980905-20151004010517

The basic characters of the original story must remain, but the impact they have on the story can be altered in whatever way you deem fit.

No, you can't remove the parents, but you can modify their presence and impact on the story to make their roles as minimalistic as possible (they were pretty minimalistic characters anyway). You can also change the bullies as much as you want, as long as they remain the same character (ie, changing their names would be a big 'no-no').