Behind Deputy Secretary of State Warren Christopher's round-the-clock effort for the American hostages is this verbal order from President Carter, arousing mixed emotions among Ronald Reagan's men: free the hostages "at all costs" before the Jan. 20 inauguration.

The admonition "at all cost" helps explain the steep U.S. raise in the hostage bidding. Although State Department officials denied the published figure of $8 billion, the actual Carter offer now stands close to it at a rounded-off $7.3 billion.

At this has chilled U.S. bankers and means more outflow ahead for the leaky U.S. Treasury. While Reagan abjures bargaining with "barbarians" andcondemns paying ransom, his foreign policy advisers would be delighted to have the hostage headache cured before he is sworn in. For Jimmy Carter, there are no doubts: if his last bid fails, he rightly fears the hostage taint will dominate history's view of his presidency.

Carter's order to win hostage freedom "at all costs" had concerned major banks holding frozen Iranian assets that would be taken over by the U.S. government for return to Iran. That mean claims against Iran for outstanding debts in the end may have to be paid by unsuspecting American taxpayers. That could delay payment to the bankers far into the future.

Nevertheless, the banks cannot intervene. "We cannot even think about tampering with such a life-or-death issue," one major Manhattan bank executive told us. "If we did, the politicians in Washington would string us up without a peep from anyone."

What has worried Carter administration officials far more than the banks is the Reagan reaction. Strenuous efforts have been made to tie Reagan to any hostage deal negotiated but not finally consummated by Carter before Jan. 20.

A top-secret White House cable to U.S. emissaries in Algeria went as far as possible to satisfy Iranian doubts about the incoming administration. If the hostages are freed before Jan. 20, is said, Secreatary of State-designate Alexander Haig would look "favorably" on the United States' carrying out the bargain pledged by Carter. A second cable used the words "probably."

Publicly, Reagan and Haig are buying nothing of the kind. Insiders declare that any deal smacking of high-cost ransom wil be subjected to intense scrutiny before Reagan agrees.

The reality is more complicated. If Carter issues an executive order unfreezing the Iranian assets, Reagan's options will be circumscribed. Besides, the onus on paying tribute for the hostages would be Carter's, not Reagan's.

There is, moreover, an additional reason for Reagan and Haig privately to welcome even an "at all costs" Carter deal of cash for hostages: ending the hostage crises would cost the Soviet Union its hostage trump card and free the U.S. hand in the Persian Gulf. Once the hostages are freed, the United States once again becomes a competitor with Moscow for future influence with one of the richest and most strategically important counntries bordering the Soviet Union.

Soviet intrigue against the United States in Iran has increasingly concerned, the lame duck president. One month ago, Carter began to worry that the Kremlin was fomentinig radical Iranian factions to block any consensus for releasing the hostages.

He asked for a thorough Central Intelligence Agency study of Moscow's true policy. But when it arrived in the Oval Office, it was a useless "maybe yes, maybe no" assessment of the Kremlin's intentions that told Carter nothing.

Reagan advisers need no CIA report. They are certain the Soviets want to perpeturate the hostage crisis in their own interest. No matter how hesitant the new president is in promoting a new U.S.-Iranian era, release of the hostages immediately ends Soviet effectiveness in poisoning relations between Washington and Iran. That could prove invaluable for Reagan in the coming battles over the Persian Gulf and its oil.

For the old president, what matters most is history's blessing. He wants it written that Jimmy Carter at the 11th hour ended one of the most disgraceful episodes in American history, whatever the cost to American taxpayers.