Pip is hot to trot. In true Sherlockian form, he's figured out who Estella's parents are, but he wants confirmation—and he knows where to get it.
He goes to Jaggers' office only to find Jaggers and Wemmick taking care of business, bills, and other items. They're not in the cheeriest of moods, but Pip is determined.
First order of business, he tells Jaggers about the money Miss Havisham has granted to Herbert's career, and he asks Jaggers to write him a check in the amounted that was agreed upon.
Mr. Jaggers and Wemmick scold Pip for not asking for money for himself.
Pip then explains that he knows who Estella's father is. When he names Provis (a.k.a. Magwitch), Jaggers is certainly surprised, but goes on with business as usual.
Pip doesn't like being ignored and he continues to rant at Jaggers and Wemmick in the hopes that they will relent and give him the information he so desperately wants.
He explains that he needs to know because he loves Estella, and, though he doesn't have a chance with her anymore, he still really cares about her.
When Jaggers and Wemmick still won't offer up any information, Pip addresses Wemmick's soft side—the Aged-loving, castle-building Wemmick. Mr. Jaggers is totally surprised to hear that Wemmick has this soft side, and things get really awkward for a minute.
Jaggers spills: he tells the story of winning Molly the housekeeper's case back in the day when she was accused of murder just at the time Miss Havisham was also looking to adopt a child.
Because he saw and sees so many orphaned children grow up to live hard lives and to become criminals, he thought he might be able to save Molly's daughter. Hey, Jaggers has a sensitive side, too!
It helps that Molly had told her husband that she had killed the child, so the husband would never know that the daughter had been adopted.
But Jaggers never knew that the father was Provis/Magwitch.
He swears both Pip and Wemmick to secrecy, telling Pip that no good can come from uncovering this secret.
Jaggers and Wemmick go back to business as usual, but things are a little awkward between them, now that Jaggers knows Wemmick is a softy. It's only when Mike, the annoying client who always wipes his nose on his fur cap, shows that the two are able to be blissfully irascible to him, and, thus, are able to restore their working relationship.