"In a move without precedent in the modern era, Republican congressional leaders... have penned a letter" to the Fed.
The shocking thing here, surely, is that no one ever did it before. Although the Fed's board of governors are appointed by the President, the Fed is not technically a part of the US Government, but it controls our money supply and -- in important ways -- the dollar itself.
Printing money is a Constitutional function of the Congress, but actually printing money isn't the way that the money supply is manipulated most of the time now; mostly it is done via actions like the Fed's "Quantitative Easing," in which purely notional transactions between banks "reduce" or "expand" the money supply. The Congress has granted the Fed authority to manipulate the money supply in that way, and so Congress has in a sense delegated its Constitutional duty to the Fed.
Since the Fed's authority is derived from Congress' authority to print money, why wouldn't Congressional leadership send a letter to the Fed telling the Fed what it thinks about the money supply? It's Congress' authority that is being used here, after all. Even if we have decided to delegate that authority to an independent board, Congressional leadership surely has a legitimate power to send a letter voicing an opinion as to how Congress' delegate authority should be used.