I recently received a message from a moderator for my "bad" reviewing queues (yes, I'm guilty of this), but is it compulsory to message back? Or does it seem slightly rude to ignore their message, but still understand what they are trying to say?
No need. You are not required to reply to a mod message unless there is something you want to clarify, something that needs to be clarified on their end or something that was done that you think shouldn't have.
Just take note of the message and avoid repeating the same mistake. That's a reply in itself :)