Settings API – format container of setting and setting’s description

It doesn’t seem possible to modify the <tr> tag, but for making it hidden by default (or initially hidden), then you can use the sixth parameter passed to add_settings_field(), which is $args:

add_settings_field(
    'my_field',           // ID
    'My Field',           // Title
    'my_field_callback',  // Callback
    'my-setting-admin',   // Page/slug
    'setting_section_id', // Section
    array( 'class' => 'hidden' )
);

So as you can see, we set the tr‘s class to hidden which applies display: none to the tr element. (hidden is an existing CSS rule in wp-admin/css/common.css which is loaded on the WordPress admin pages).