The doctor's story of the shadows ship on Mars was interesting, although I'm wondering why Garibaldi didn't mention that he saw something like this to sheridan before this woman brought it up.
Garibaldi and Sinclair were the only two who knew prior to this. Sinclair was on Mars at the same time as Garibaldi; that's where they met. (This is elaborated upon in the comics that were published during season two.) Garibaldi didn't have any other evidence beyond the badge so they kept it secret. IIRC, in the comic he just tells Sheridan that he found a piece of evidence, without identifying what it was. There wasn't anything else for Garibaldi to do until the news came around in this episode that Earth was after the ship on Ganymede and his story was corroborated with Dr. Kirkish.