in your subtemplate, you have itemform.php
To remove the field,
remove the line 237 and 238
<input type="text" name="existingImage" id="existingImageValue" class="text_area" readonly />
<input type="button" value="<?php echo JText::_('K2_BROWSE_SERVER'); ?>"id="k2ImageBrowseServer" />
These are the line that is used to browse the server