I've a feeling I once needed to do this - albeit quite a long time ago, so my memory's a bit hazy...
Look in TortoiseGit->Settings->Git->Remote and you'll see your library's current URL. You might need to experiment a bit but basically, you just need to replace it with the appropriate path (or set the appropriate path as your Push URL). I can't remember now if a simple path worked okay or if I needed to precede it with File:/// - though I'm sure I managed to make it work.