Hi,
The only way to remove the tab indexes is by editing the core plugin files. Please note, by removing those tab indexes the magnifier icon will not be selectable – those explicit tab indexes were used to make it more accessible.
The file you need to edit is wp-content/plugins/ajax-search-pro/includes/views/asp.shortcode.probox.php lines 38 and 79. If you simply remove those attributes, it will resolve the issue.