The back and forth between Target and an investor group is getting even messier with less than a week until the company's board election.

Today, Nominees for Shareholder Choice, a group associated with hedge-fund manager William Ackman, issued a press release calling for two Target directors to step down immediately.

A rule in the company's governance guidelines says any director whose "affiliation or position of principal employment changes substantially after election to the Board will be expected to offer to tender his or her resignation as a director promptly to the board." A committee can then decide whether to accept the resignation.

Ackman's group say based on that rule Anne Mulcahy, who recently stepped down as CEO of Xerox, and Solomon Trujillo, who has been asked to resign as CEO of an Australian telecommunications company called Telstra, should resign and make room for "directors with relevant experience and fresh perspectives."

The statement takes particular aim at Trujillo, highlighting a recent article in The Australian IT that is critical of his term at Telstra:

"The Sol Trujillo era at Telstra will be characterised by $15 billion of shareholder value destruction, uncertainty around the outcome of his much-heralded transformation program and customer satisfaction at an all-time low."

Ackman has publicly sparred with Target since 2007, when his hedge-fund acquired just under a 10 percent stake in the company. After unsuccessfully pressing the retailer to spin-off its real-estate into a separate company, Ackman is seeking to elect himself and four others in the company's board election on Thursday.