In February, Exxon Mobil sued the U.S. investment firm Arjuna Capital and Netherlands-based green shareholder firm Follow This to keep a shareholder resolution they sponsored from appearing on the agenda of its May 29 annual meeting. The resolution urged Exxon Mobil to work harder to reduce the greenhouse gas emissions of its products.

The company’s legal threat worked: Days after the lawsuit was filed, the shareholder groups, weighing their relative strength against an oil behemoth, withdrew the proposal and pledged not to refile it in the future.

Yet even though the proposal no longer exists, the company is still pursuing the lawsuit, running up its own and its adversaries’ legal bills. Its goal isn’t hard to fathom.

“What purpose does this have other than sending a chill down the spines of other investors to keep them from speaking up and filing resolutions?” asks Illinois State Treasurer Michael W. Frerichs, who oversees public investment portfolios, including the state’s retirement and college savings funds, worth more than $35 billion.

In response to the lawsuit, Frerichs has urged Exxon Mobil shareholders to vote against the reelection to the board of Chairman and Chief Executive Darren W. Woods and lead independent director Joseph L. Hooley at the annual meeting.

He’s not alone. The $496-billion California Public Employees’ Retirement System, or CalPERS, the nation’s largest public pension fund, is considering a vote against Woods, according to the fund’s chief operating investment officer, Michael Cohen.

“Exxon has gone well beyond any other company that we’re aware of in terms of suing shareholders for trying to bring forward a proposal,” Cohen told the Financial Times. “There doesn’t seem to be anything other than an agenda of sending a message of shutting down shareholders’ ability to speak their mind…”