There's a simple way to stop this from happening. Somewhere in your initialization method, you can include this statement:
// by default, MQExceptions are logged on System.err
// this will switch off that behaviour
MQException.log = null;
Of course, you can - and should! - still catch and handle the exceptions as normal, and get at the text of the exception if required. This just prevents them from always being printed on the console (or location of System.err).