Can other countries central banks impact the decision of the Federal Reserve? In theory, the Federal Reserve enact policies that will benefit the country, but given the dollar's reserve currency, it's policies will have wide-reaching impact. Can other central banks impact the policy decision of the Federal Reserve. If so, through what mechanisms can the other central banks influence the policy decisions of the Federal Reserve?
They can, and they do every day.
Globally, economies are linked together through trade. One nation's monetary, trade, or even domestic industrial policies can have impacts that ripple through the economies of other countries.
When the Federal Reserve Board and it's subordinate entities meet to consider policy, their goals are known as the "Dual Mandate" which is to help reduce unemployment as low as is practicable, and also to keep the "price level" (a general measure of central tendency among all traded goods and services) at as stable a level as possible.
When other central banks make choices, those choices change the landscape for the U.S. economy, and those changes are part of the overall picture that the FRB has in mind when it makes decisions.
The Federal Reserve's own site calls out the ways in which other nations' central banks tend to share policy openly, helping them to understand how the other players on the global economic 'team' are setting up their own moves. This is also a form of influence, and all-but-direct communication. An example from the link (emphasis added):
Most other major central banks also publish forecasts of inflation and other macroeconomic variables. A well-known example is the Bank of England's Inflation Report, which provides forecasts for economic growth, the labor market, and inflation together with an assessment of the uncertainty associated with each forecast. ... With regard to the goals of policy, the Federal Reserve and other major central banks state the objectives of monetary policy clearly and publicly and explain how the policy committee pursues those goals.
So while diplomatic channels may not be open to domestic financial ministries, the metaphor here is people being told they can't talk to each other, and so they resort to very loudly talking to their own cohort such that they can be overheard.