Updated from 12:31 p.m. EDT

Hedge funds Jana Partners and SAC Capital aren't backing down from their agitating at TD Ameritrade ( AMTD - Get Report).

The funds, which have been pushing the online broker to pursue a sale with a competitor such as Charles Schwab ( SCHW - Get Report) or E-Trade Financial ( ETFC - Get Report), sent a letter to Ameritrade's board Tuesday requesting further changes in the company's approach to evaluating a deal.

On Monday, Ameritrade announced that its board voted to exclude representatives of its two largest shareholders from potential buyout talks as a result of requests by Jana and SAC. The hedge funds had argued that big shareholder Toronto-Dominion ( TD - Get Report), which owns a 40% stake in Ameritrade, had too much influence on M&A talks and could nix a sale if it diminished the Canadian bank's position in the U.S.

In the past, Toronto-Dominion officials have denied any conflict of interest.

Ameritrade's mergers and acquisitions committee had consisted of five members: three outside independent directors; Wilbur Prezzano, a representative of Toronto-Dominion Bank; and Robert Slezak, a representative of the Ricketts family, which owns about 21% of the company and is its second-largest shareholder.

With Ameritrade's move Monday, Prezzano and Slezak were removed from the newly organized M&A board.

Now Jana and SAC, which own a combined 8.4% of Ameritrade shares, are asking that Ameritrade allow the independent directors on its merger board committee to be "exclusively empowered to pursue and lead discussions with" potential acquirers, the letter says.

A TD Ameritrade spokeswoman declined to comment on the funds' missive.

The funds called the removal of Prezzano and Slezak a good first step, but said they will continue to be vigilant as the company looks to find strategic options.

"We will therefore continue to review the situation to determine whether the conflicts we have raised, and will continue to examine, have in fact been sufficiently addressed," said the funds' letter, which was signed by Jana head Barry Rosenstein and SAC Capital's CEO Steve Cohen. They added that they would contact the independent directors appointed to "share our views regarding the strategic options available to the company."