Giannini is Blomkvist's sister and Salander's lawyer. She completely rocks for the whole book. She's a women's rights lawyer and doesn't, at first, feel qualified to represent Salander. But, not only does she save Salander from possibly being murdered by a nutso secret agent, she also presents Salander's case flawlessly in court. She's an important player in the overall triumph of justice we find in The Girl Who Kicked the Hornet's Nest.
And it's not easy. For half the book, she's entirely out of the Blomkvist-Salander loop. As per usual, those two are keeping secrets. She doesn't seem personally offended by the secrecy, just irritated because she doesn't have all the facts she needs to do her job. Eventually, she and Salander do develop a measure of trust, but their relationship is rather rocky and gruff. Here's an exchange from the end of the book:
Salander: "I don't want any inheritance from my father. Do whatever the hell you want with it."
Giannini: "Wrong. You can do what you want with the inheritance." (Epilogue.39)
There's something Bugs Bunny-style funny about all this, but interactions between Salander and Giannini show us just how difficult it can be for Salander to communicate sometimes. It's not entirely clear how she feels about Giannini. The fact that she keeps her on as a lawyer, and even shares with Giannini her top-secret address, suggest she probably likes her a lot. Like Salander, Giannini herself is a bit out of reach. She appears to be a caring person and a brilliant lawyer. But, we don't go deep into her character.