You could draw a new linestring and then use the Append Tracked function to add the piece(s) you want to keep and skip over the pieces you want to throw out. Then delete the original line you no longer need.
I am not clear from your pictures above what you are trying to do - the first picture shows zero data along the line that you say in the second picture that you want - is it just a straight line between the ends of that gap that you want to create?
If yes then create a New Linestring, click on the start of the Red Line, then use Append Tracked, click on the orange line and then start where the end of the red line is to keep that section. The append Tracked is a button in the header of the Linestring command
Alan