You can remove (turn-off) the Welcome screen by using any of these two options:
Single:
add_action( 'load-index.php', 'hide_welcome_screen' );
function hide_welcome_screen() {
$user_id = get_current_user_id();
if ( 1 == get_user_meta( $user_id, 'show_welcome_panel', true ) )
update_user_meta( $user_id, 'show_welcome_panel', 0 );
}
?>
Multisite:
<?php
if ( ! defined( 'ABSPATH' ) || ! is_multisite() )
return;
add_action( 'load-index.php', 'hide_welcome_screen_for_multisite' );
function hide_welcome_screen_for_multisite() {
$user_id = get_current_user_id();
if ( 2 == get_user_meta( $user_id, 'show_welcome_panel', true ) )
update_user_meta( $user_id, 'show_welcome_panel', 0 );
}
?>
The state of the welcome panel is stored in a usermeta key that is global to the network. The value of 0 means the welcome panel should not be shown (and has been dismissed).
The value of 1 means the welcome panel should be shown. (The initial user for a ingle-site WordPress install is given this value) .
The value of 2 is specific to multisite, and means that the panel should only be shown if the user is the site owner.
Once dismissed, the panel can be shown by visiting the Screen Options tab.
I hope that helps.