You can edit the file /plugins/system/docker/themes/default.php and replace the codes below,

[gist]
<?php if (($this->isMobile() && !$this->my->id) || !$this->isMobile()) { ?>
<div class="docker-popup-container">
<div class="docker-border--right docker-border--bottom docker__search">
<div class="docker__search-box" data-docker-search>
<form action="<?php echo JRoute::_('index.php');?>" method="post" class="docker__search-form">
<input type="text" name="q" class="docker__search-input" autocomplete="off" data-nav-search-input placeholder="<?php echo JText::_('COM_EASYSOCIAL_TOOLBAR_SEARCH', true);?>" />
<?php echo $this->html('form.itemid', ESR::getItemId('search')); ?>
<?php echo $this->html('form.token'); ?>
<input type="hidden" name="controller" value="search" />
<input type="hidden" name="task" value="query" />
<input type="hidden" name="option" value="com_easysocial" />
</form>
</div>
</div>
</div>
<?php } ?>
[/gist]

With,

[gist]
<?php if (($this->isMobile() && !$this->my->id) || (!$this->isMobile() && $this->my->id)) { ?>
<div class="docker-popup-container">
<div class="docker-border--right docker-border--bottom docker__search">
<div class="docker__search-box" data-docker-search>
<form action="<?php echo JRoute::_('index.php');?>" method="post" class="docker__search-form">
<input type="text" name="q" class="docker__search-input" autocomplete="off" data-nav-search-input placeholder="<?php echo JText::_('COM_EASYSOCIAL_TOOLBAR_SEARCH', true);?>" />
<?php echo $this->html('form.itemid', ESR::getItemId('search')); ?>
<?php echo $this->html('form.token'); ?>
<input type="hidden" name="controller" value="search" />
<input type="hidden" name="task" value="query" />
<input type="hidden" name="option" value="com_easysocial" />
</form>
</div>
</div>
</div>
<?php } ?>
[/gist]