By Gregor Stuart Hunter SINGAPORE (Reuters) -The U.S. dollar regained its footing in early Asian trading on Thursday after the U.S. Supreme Court said it would hear arguments in January over President Donald Trump's attempt to remove Federal Reserve Governor Lisa Cook, leaving her in the post for now. Market concern about the Fed's independence now "moves to the backburner for the next few months," said Tony Sycamore, market analyst at IG in Sydney. The dollar's broader index measure against a basket of key currencies edged up 0.1% to 97.80, retracing declines after four straight days of losses, as traders pondered the length of the U.S. government shutdown and its effect on economic data releases. "We're in a bit of a void," Sycamore added. "We're effectively done now, in terms of market-

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