I also just needed to alter this to remove anything being added between and having seen it wasn’t an option, went and looked myself. If you open up faster-image-insert.php in your plugin directory and scroll to line #389, you see the following:
if(is_string($_POST[ $customstring ]) && !empty($_POST[ $customstring ])) $cstring = $_POST[ $customstring ]; else $cstring = "<p></p>";
If you comment that line out with “// ” at the beginning of it, the plugin will no longer insert paragraph tags in when you leave the field empty. Hope this helps!