BUDs is an abbreviation for Basic Underwater Demolition/SEAL., a Navy training and selection program that lasts 24-weeks, designed to develop candidates for the Navy's elite Sea, Air and Land force.
The BND is Germany's intelligence agency, also known as Bundesnachrichtendienst.
When Jack tells Greer, "This isn't TFAD," he's referring to the Terror, Finance, and Arms Division from Season 1. Jack reported up to Greer at TFAD, which is part of the CIA's Counterterrorism Center.
The title is Latin for "Third Option", which is a reference to the President having a third option if diplomacy or military action fail or are not feasible.
The San Esteban Jungle featured in Season 2 of Tom Clancy's Jack Ryan is one of Venezuela's protected national parks. The forest spans approximately 275 square miles (445 square kilometers).