What you are fighting with is definitely a border. Some strange things with the border you were fighting with:
When you select the lines above and below, in borders and shading it will show that the borders are set to none. If you still click on None, even though it says it's already there, it should clear the border.
Second, borders don't like when you try to delete them using the delete key. If you try using the delete key before the above method, like you did, then the above method doesn't work right any more, unless you select everything.
Steve