Translation:She is Mr. John's grandmother.
The alternative answer said "Mr. John" but we wouldn't use Mr. with a given name.
I quite agree, honorifics would not be used with a given name. While I found there was Mr. or Ms. John as a surname.
It would be recommended to us a name which is exclusively used as a surname, e.g. Smith, Brown, Robertson etc., to avoid misunderstanding of learners.
See, this is a problem - in this sentence, the system wants "Mr. John," however, in another, reverse sentence, it asks for just "John," but marks you incorrect if you leave off the "San."
I cannot, for the life of me, distinguish between Japanese aunt or grandmother.
is it ok to use "彼女" in this case? wouldn't "この女の人" be more respectfully?
Yes, you can use 彼女 in this case, thus 彼女はジョンさんのおばあさんです is equally correct. この女の人 is neither respectful nor derogatory, just neutral. This may be literally translated as ”this woman/lady".
If you want to say it more respectfully, use こちらの女の方 or こちらの女性の方. Generally 方 (kata) is an honorific expression of 人.