Is there a way to turn off or turn down the volume of "mute on/mute off" messages while you're a on Lync phone call?  It's typical for me to mute myself when I'm not speaking to reduce noise; however, this announcement is so loud that I miss parts of the conversation when others are speaking.

I'm using a Jabra headset... not sure if that is part of the problem as well?

Please help. I've resorted to having to be strategic now when muting (i.e. wait for coughs or long pauses) but I'm sure there's a better way.

Thanks.

Not supported I don't think, but the audio file you're after is here:

\Program Files\Microsoft Lync Server 2013\Application Host\Applications\Conferencing Announcement\Media\en-US

I've hacked them before with success: http://www.skypeadmin.com/2014/10/06/customize-dialin-conference-attendant-prompts-audio/

Please note that the directory about and the directory referenced in my link are different directories. 

There is no other way to change the volume or content of these messages that I'm aware of. 

So, can this only be changed on the Server side -- not by the users on the client side?

Correct.