Within 'git add -p' when you get to the hunk that you want to edit (split down to single lines), press 'e'. This will open an editor (vim in my case) which lets you edit the diff manually.
In there you can remove added lines (prefixed by '+') by removing them, and re-adding removed lines (prefixed by '-') by replacing the '-' with a space ' '.
In there you can remove added lines (prefixed by '+') by removing them, and re-adding removed lines (prefixed by '-') by replacing the '-' with a space ' '.