It appears that the NAME and HITS column are always on by default so I am not sure if you would be able to hide this column through modifying the control. However, you can do this through jQuery which I have included below:

$('td:nth-child(COLUMNNUMBERHERE)').hide();

The COLUMNNUMBERHERE should be changed the order number of the column you wish to hide. For example if the NAME column is the first one that appears on the table then it should be:

$('td:nth-child(1)').hide();

For multiple columns, such as the one you are requesting, you would need to separate each column by using a comma (using NAME as the first column and HITS as the fifth column):

$('td:nth-child(1),td:nth-child(5)').hide();

The is jQuery should be added to the bottom of the CustomSearch.aspx page right before the closing </body> tag:

<script type="text/javascript">
$('td:nth-child(1), td:nth-child(5)').hide();
</script>
</body>

Once you have added it, save the page and run your query again.This has been tested in WebLink 9 and works as expected.

Hope this helps!