This line of code definitely causes the problem that described on Internet as:
“all apostrophes and quotation marks are prefixed with backslashes”.
I liked the solution with writing a new plugin with this code in it:
<?php
/* Plugin Name: Strip Slashes */
add_filter('pre_topic_title', 'stripslashes', 40);
add_filter('pre_post', 'stripslashes', 40);
add_filter('bb_add_topic_tags', 'stripslashes', 40);
?>
Does it work? – Yes!