Check on Dante and Beatrice. How is this famous couple reflected in the story?
I'm not sure there's a huge connection between Dante and Beatrice and the characters in this story; but there is, as you mentioned, a reflection.
Dante had a life-long obsession (in a most Medieval, non-stalker way, I gather) with a woman named Beatrice. There was, apparently, very little actual contact between them; however, Dante did see her as his muse. He wrote poetry about her and included her in his Inferno (she was in Eden, of course). In Dante's final work, it is Beatrice who leads him to Heaven.
So, how does that reality translate into this story? Giovanni falls in love with her, and I suppose one could call love an obsession. While they are connected on many other levels, there is no actual physical contact between them. Hawthorne's Beatrice is no one's muse, and her strongest connection is to her "sister" plant rather than another human being. While Beatrice does live in a garden, it's certainly not the garden of Eden; and while Giovanni does love her, he writes no poetry rhapsodizing about her.
The fact is that Beatrice, to any who have done some classical reading, conjures up an image and a story which is far more impactful on this short story than the connection between Dante and Beatrice. This is Hawthorne's story, and he seems to have drawn some sort of inspiration from her, not particularly from Dante.