I discovered this by accident, but in my documents with tables and the paragraph mark that cannot be deleted, I found a hidden section break in the table.

I don't know how it got there -- maybe a cut and paste issue from another document.

1. In the table that precedes the paragraph mark, create another empty row (I just hit Tab).
2. Select the entire row and ONLY that row of the table.
3. Go to Table Tools>Layout>Convert to Text.
4. Convert that row to text and voila - you should see that hidden section break appear.
5. Delete the section break and the paragraph mark as well.

CAUTION: Deleting that section break might impact your headers and footers, if you have them in the your document. Be prepared to fix those.