Hide profile icon when using Profile in listing mode
Yes, there are at least two ways to disable this icon that I can think of. 

The first is not very authentic, but requires less work and code modification. You use CSS to avoid the display of the icon. You'd need to include in your CSS file something like:

.crm-profile-name-&lt;your-profile-name&gt; .Individual-icon {
display: none;  }


Also, you'd need to repeat the CSS selector to Organization-icon and others types of contacts if that's your case. Mind that one can make the icon show up in the browser changing the CSS on the fly and so, would access the overlay information if it is still there. So, this method is not good to secure the data, you should first be sure that data is correctly protected, not showing up publicly in the overlay box.

The second method is much more gentile, but requires you to change the Listing template code. It's referenced by Dave Greenberg in this thread and the code stills work nice, I just tested it.

If you have never customized templates, I would say you should first read this page, as I'd be too long to explain every step to do this here. 

Once you are good to go, copy the file civicrm/templates/CRM/Profile/Page/Listings.tpl to your custom templates directory, keeping the folders structure. Edit the file from line 59 to look like this:

    &lt;table&gt;
      &lt;tr class="columnheader"&gt;
      {foreach from=$columnHeaders item=header name=headers}
        {if $smarty.foreach.headers.iteration GT 1}
        &lt;th scope="col"&gt;
        {if $header.sort}
          {assign var='key' value=$header.sort}
          {$sort-&gt;_response.$key.link}
        {else}
          {$header.name}
        {/if}
         &lt;/th&gt;
        {/if}
      {/foreach}
      &lt;/tr&gt;

      {counter start=0 skip=1 print=false}
      {foreach from=$rows item=row name=listings}
      &lt;tr id="row-{$smarty.foreach.listings.iteration}" class="{cycle values="odd-row,even-row"}"&gt;
      {foreach from=$row key=index item=value name=cells}
        {if $smarty.foreach.cells.iteration GT 1}
        {if $columnHeaders.$index.field_name}
          &lt;td class="crm-{$columnHeaders.$index.field_name}"&gt;{$value}&lt;/td&gt;
        {else}
          &lt;td&gt;{$value}&lt;/td&gt;
        {/if}
        {/if}

      {/foreach}
      &lt;/tr&gt;
      {/foreach}
    &lt;/table&gt;
    {/strip}
    {include file="CRM/common/pager.tpl" location="bottom"}
    &lt;/div&gt;
{elseif ! $isReset}
    {include file="CRM/Contact/Form/Search/EmptyResults.tpl" context="Profile"}
{/if}


This would make the column of profile overlay icon to go away.

Also, in an that old Forum thread there were a word from Dave Greenberg saying that setting all Summary Overlay profile fields visibility to 'User and User Admin' would disable the overlay, but in the actual CiviCRM version, this profile is reserved, so you can't change the visibility of the field. Hence, the above methods looks necessary to me.