In discussions of the "credit channel" in the transmission of monetary policy, I've read that increasing the policy rate reduces bank reserves. Can someone explain how this happens?
It's a direct result of how monetary policy is normally conducted. In normal-times monetary policy, the Fed will increase its target rate (the Fed Funds rate) by selling Treasuries to dealers, who will pay for them by withdrawing deposits they hold at banks. The cash that formed these deposits can therefore no longer be held as excess reserves at the Fed, which decreases the supply of funds in the Fed Funds market, increasing the price of borrowing funds (i.e., the Fed Funds rate). The reduction in bank reserves is actually the mechanism by which rates are increased; the sale of bonds is just a way of reducing reserves.
Here's a reference.