You'll notice that when you hover over a row reference or lookup column, a card pops up with information about that row.
The columns (or fields) that are visible on the card match the visible columns on the base table where that row lives. This means that if you hide/show a column on the base table, it will also be hidden/shown on the hover card.
Remember to hide/show columns on the base table (the hover cards ignore views of that base table).
Here's a quick example:
