The LOTGK says she "salutes" the giants which suggests they either outrank her in power or are equally powerful in their own realms.

"salute" at its simplest means greet. 

Lewis uses its medieval meaning, which can involve a kiss of greeting, as well as a mark of respect. It comes from Latin word, which has a suggestion of wishing the person good health. 

The LOTGK has a good relationship with giants, and perhaps she addresses them in a respectful way, but I doubt she has respect for them.

...Ok I know this theory has already been addressed and dismissed, but I do have a personal soft spot for the possibility that she's Jadis' daughter, taking revenge for her mother. As to who would be willing to have a child with an ice witch - Jadis is repeatedly said to be beautiful, and also I could see many evil-alligned creatures caring more about sucking up to power than having a *good* mate?

Another possibility I would be willing to accept, re: her and Jadis being of "the same crew", is the possibility that Jadis trained and indoctrinated a cult of witches of other species origins while she was in the North, and LOTGK is the last survivor or descendant of this cult.

Another thought I've run into that I find amusing, although less resonant than the previous possibilities, is that LOTGK is actually snakey rather than humanoid by her birth nature, and a witch took her in as a familiar/assistant and taught her to shapeshift.

@silverlily Interesting ideas! I don't think it's completely "against canon" that the Green Witch could be a family relation of Jadis — it's just that they couldn't be the same person, going by what we know from the books. But "one of the same crew" could very well mean they are literally related. Going by the very little we know, it's not outside the realms of possibility that Jadis could have had a daughter, perhaps fathered by one of the other evil creatures she may have met during her time in the North before she re-invaded Narnia as the White Witch. Maybe the Green Witch's father was also a humanoid who could turn into a snake, or a snake who could turn into a humanoid...

Or else (given the stretch of over 1,300 years between Jadis's final defeat in LWW and the Green Witch's reign in SC), maybe the Green Witch could be a later descendant — a granddaughter or further down — since we don't know whether she herself was immortal in the way Jadis became after eating the apple. But again, there's nothing to suggest they couldn't have been related "by blood", or that they didn't know each other in the distant past, if the Green Witch was also immortal (unless killed in battle) or at least very long-lived.

Posted by: @silverlily

Another thought I've run into that I find amusing, although less resonant than the previous possibilities, is that LOTGK is actually snakey rather than humanoid by her birth nature, and a witch took her in as a familiar/assistant and taught her to shapeshift.

I'd never thought of that idea, but I reckon it's not outside the bounds of possibility either! I sometimes wish Lewis himself was still around for us to bounce all these questions off him and I wonder what he'd say — hopefully something more interesting than "Oh, gosh, even I don't know — I never thought about it that far myself..."   (He was very happy to answer young fans' questions about Narnia when they wrote to him during his lifetime, and there's a book of his letters to children, but unfortunately I don't think any of them deal with this particular question!)