Hey, that's OK. Do you know you can convert Type into a Shape from the Type menu? If you made two copies of the G Type layer, and went Menu > Convert to Shape. The with the Path selection tool (the black arrow) draw a box around the unwanted points and delete them. You obviously know you can use the Direct selection tool to manipulate individual points on the path.
Even if you end up with a raster logo, it would have a very clean outline, and you could convert it back into a Shape from the Paths panel. But you shouldn't need to rasterize.