So no, the text is correct. But obviously it's wrong. It doesn't ONLY mute the keyboard, it mutes everything for the person typing. The keyboard, the person, the squeaking chair.
edit: in fact I would go so far as to say that the majority of English speakers, at least here in America, would prefer saying "mute the mic" instead "put the mic on mute" (I've never heard anyone say the latter in actual conversation, to be honest).
Most UIs show a microphone, that you can click on to disable. A circle with a slash through it will appear on top of the picture of the microphone. This is referred to as "muting."
This should be enough to see why it is called "muting your microphone." While you could say "disable your microphone," this can lead to confusion, such as thinking that you are talking about more permanently disabling it, such as you do in your computer settings.
The most important thing about language is that it is understood. "Mute your microphone" is going to be understood.