Once your table is selected, it should be highlighted, as shown below.
From the Table
Design tab, Borders group, you'll select the Borders button
list arrow, which will open several options. Select No Border, which will remove all borders from your table.
To insert some borders:
1. Select a range of cells, or click in a specific cell.
2. Click the desired border to apply in selected cells.
*You can see that top and bottom borders were added to row 1, as well as a bottom border to the last row of the table.