"She is Mr. John's grandmother."
Is the "Kanojo ha" really necessary? I left it out of my translation but was marked wrong
It shouldn't be necessary. That's something that can be left out in spoken Japanese depending on the context.
かのじょはジョンさんのおばあさんです。She is Mr. John's grandmother. ジョンさんのおばあさんです。It is Mr. John's grandmother.
Both are acceptable sentences, but the original sentence used "she", so only the first is correct.
Formality level. If you're talking to someone who isn't part of your family, you'd usually refer to your own grandma with the less formal そぼ and someone else's grandmother by the more formal おばあさん. You're speaking humbly about your own family and politely about other people's families.