When you run a Cygwin update, it should by default update all packages that have changed, which should give you the latest C library. A lot of "shoulds", but I've never had any issues.
However, this sounds like an error from the client program, running on a remote host, not the X server (which is running under Cygwin). I'm not sure how a Cygwin program would even report this.
Please edit your question, showing the actual program that you're running, and the exact text of any error message -- copied from either the console window or a dialog box.