The Republic wanted the Exile and the reason they went to Telos is probably because it was the closest Republic world. Before they can speak to the Exile however, she escapes Citadel Station. The Republic then changes it's mind and lets the Exile wander freely ("[...]the Republic has decided not to detain the Exile, and adopt a wait-and-see approach."). My guess to why they did this is:
They wanted her to find the rest of the Jedi. They knew that without the guidance of the Jedi, they could never defeat the sneaky Sith forces and keep the Republic from collapsing at the same time. What they didn't know was of course the threat Nihilus posed if they were to meet in large numbers again.
On Wookieepedia it says that it was Atris that orchestrated the Exile's return to known space, and the source is the KotOR Campaign Guide. I don't remember any of that being implied in the game, though.