getting rid of overlapping lines / dots

when for example i draw a face and on the same drawing i draw the hair over, there’s an interlapping of lines, meaning 2 lines connect to same dot. if i try to get rid of dots then more will appear and if i alreay have filled the face with color it will go bad.

some example
i have 2 dots and an oval (dot -line above, line below - dot)
i want to get rid of the superior line that connects the 2 dots
and leave just 2 dots with one line between, and in easy steps

cheers & thanks

The easiest way to get this result is to do it while the oval is not filled with color.

To remove the top line: