I dont have many relatives. Found one on Facebook. Her Grandfather’s Brother ( Her Great Uncle) married my Mother’s Sister (my Aunt).
Relationship? 
I think I’d just go with ‘cousin’. If I had to guess, I’d say second cousin, once removed?
They are not cousins, since they don’t share any ancestor in common.
In fact, you are not really directly related, the only relationship being through marriage. Your aunt is the sister-in-law of her great uncle. Her great-uncle is the brother-in-law of your mother. There aren’t really simpler terms for this.
Now in practice, it’s common to refer to any older relative that’s not directly related to you as aunt or uncle, and any younger member of your extended family as cousin. So you could refer to her grandfather as your uncle; she could refer to your mother as her aunt; and you could call each other cousins; but that wouldn’t technically be correct.
I once met my brother’s sister-in-law’s husband’s brother. We decided we were unrelated.
- Insert Dark Helmet/Lone Starr joke here.
None.
You could call yourself a cousin by marriage if you wanted, but you are not related to her.
I think “Shirt Tail Cousin” is the correct term.
I was afraid of this. It’s kinda hard having no relatives closer than a cousin (and my half-Brother). 