I had the same problem before too. I mistakenly put a line across my table that I needed to be removed. I ended up deleting the whole table and starting over again. I apologize it didn't help..
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The line you are referring to in Acrobat.com Tables is a "summary row." To delete it you'll need to select and delete all the rows after the summary row. This will result in deletion of the line / summary row.
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