Options store values, and the plugin you’re trying to adjust has committed the cardinal sin of storing PHP serialised data in the database, complete with all the security and maintenance problems that come with it.
You won’t find any WordPress APIs that let you update or add to that serialised value, but you can deserialise it, modify it with standard PHP language stuff, then serialise it again. A bit like removing a box, putting something new in it, then putting it back where you found it.
$serialised = get_option( 'foobar' );
$data = maybe_unserialize( $serialised );
// .. do something with $data
update_option( 'foobar', serialize( $data ) );
How might you modify it? The same way you would any other PHP array or object, e.g.:
// if this was $data
$data = [ 1,2,3,4,5];
// then lets add a 6th item to the array
$data[] = 6
As for the specifics of this plugin/themes stored data, you’d have to contact them if you encounter issues or refer to their documentation