How to add / remove columns in Woocommerce admin product list

this table view is used by many plugins and wordpress itself. You have to check the column name. $columns['tags'] is the tag in Wordpress Post View, not in Woocommerce!

Here is a list of some $columns used by Woocommerce:

$columns['cb']  
$columns['thumb']
$columns['name'] 
$columns['sku'] 
$columns['is_in_stock']
$columns['price']
$columns['product_cat'] 
$columns['product_tag']
$columns['featured']
$columns['product_type']
$columns['date']

and that is the correct filter to apply these removals.

add_filter( 'manage_edit-product_columns', 'change_columns_filter',10, 1 );
function change_columns_filter( $columns ) {
unset($columns['product_tag']);
unset($columns['sku']);
unset($columns['featured']);
unset($columns['product_type']);
return $columns;
}

The filter manage_edit-{post_type}_columns is only used to actually add the column. To control what is displayed in the column for each post (product), you can use the manage_{post_type}_posts_custom_column action. This action is called for each custom column for every post, and it passes two arguments: $column and $postid.

Using this action is quite easy, you can find an example to display the custom field "offercode" below:

add_action( 'manage_product_posts_custom_column', 'wpso23858236_product_column_offercode', 10, 2 );

function wpso23858236_product_column_offercode( $column, $postid ) {
    if ( $column == 'offercode' ) {
        echo get_post_meta( $postid, 'offercode', true );
    }
}

You could also use a plugin to control this behaviour, such as Admin Columns.

In case someone wants to insert in a certain order, here is how to add the column to be right after Price:

add_filter( 'manage_edit-product_columns', 'wootix_show_product_order', 15 ) ;

function wootix_show_product_order( $columns )
{
    //add column
    $arr = array( 'wootix_credit' => __( 'Credits', 'wootix' ) ) ;

    array_splice( $columns, 6, 0, $arr ) ;

    return $columns ;
}

If you additionally want to sort the columns (as shown above, your column will just be attached to the end), you can do something like that in your hook of "manage_edit-product_columns" (example is taken from a class I've implemented):

const BACKEND_PRODUCT_GRID_FIELD_SORTORDER = [
    'cb',
    'thumb',
    'name',
    'pa_size_text',
    'sku',
    'is_in_stock',
    'price',
    'product_cat',
    'product_tag',
    'featured',
    'product_type',
    'date',
    'stats',
    'likes'
];

/**
 * Registers new columns for the backend products grid of Woocommerce.
 * Additionally it sorts the fields after
 * self::BACKEND_PRODUCT_GRID_FIELD_SORTORDER. Fields not included in
 * self::BACKEND_PRODUCT_GRID_FIELD_SORTORDER will be attached to the end of
 * the array.
 *
 * @param array $aColumns - the current Woocommerce backend grid columns
 *
 * @return array - the extended backend grid columns array
 */
public function add_columns_to_product_grid( $aColumns ) {
    $aColumns['pa_size_text'] = __( 'Unit size', 'intolife_misc' );
    #unset($aColumns['thumb']);
    $aReturn = [];
    foreach ( self::BACKEND_PRODUCT_GRID_FIELD_SORTORDER as $sKey ) {
        if ( isset( $aColumns[ $sKey ] ) ) {
            $aReturn[ $sKey ] = $aColumns[ $sKey ];
        }
    }

    /**
     * search additional unknown fields and attache them to the end
     */
    foreach ( $aColumns as $sKey => $sField ) {
        if ( ! isset( $aReturn[ $sKey ] ) ) {
            $aReturn[ $sKey ] = $sField;
        }
    }

    return $aReturn;
}