The image has been anti-aliased and those parts haven't been made transparent. Either you're using one of the "Soft" line tools in your program, your program isn't very good or it's a copy/pasted image.
Try using the "Magic wand select" with some level of tolerance or feather, which should select those parts to delete. Preferably feather, as that should make the edges of it partially transparent (properly) and blend it with the face colour you pick.
