Rows are selected like that:
$book->getBookGenreToBooks()->???()
I want to change the column «checked» of all selected rows.
Your given solution in your answer is very inefficient since it creates for each update a new query. A better way is to do all changes in one query:
BookGenreQuery::create()
->filterByBookId($book->getId())
->update(array('Checked' => 1));
I don't know how exactly your relations and fields are named by you should get the idea behind it.