Press This for Page

The press_this_save_post filter can be used to change the post type from post to page. Add the following code to your theme’s functions.php or a plugin:

add_filter( 'press_this_save_post', 'wpse244633_press_this_save_post' );
/**
 * Filter the post data of a Press This post before saving/updating.
 * 
 * @param array $post_data The post data.
 * @return array 
 */
function wpse244633_press_this_save_post( $post_data ) {
    $post_data['post_type'] = 'page';

    return $post_data;
}