Criticism of Harvard University is coming from an unusual quarter: postal workers.

The American Postal Workers Union is calling for President Drew Gilpin Faust to resign her seat on office supply store Staples’ board of directors if she won’t criticize the company.

The attack on Faust, who usually makes news only when she wants to, is an unlikely extension of the union’s fight with the United States Postal Service. But Faust is apparently the first sitting Harvard president to serve on a corporate board.

In particular, the union has rallied around the idea that the postal service is trying to outsource some of its jobs because of a deal it struck last year with Staples to offer mail service in the company’s stores.

Under the deal, which has since been scaled back amid union pressure, Staples employees – not unionized postal workers – would be handling the letters and packages...