I've seen reference to the term, "listen literally" as a part of NLP (Neurolinguistic Programming), which deals with communication and influence. I have my own definition that works within the context of dealing with angry and difficult people.
Understanding We "Tint" Our Listening
When we think we are listening, to some degree, in fact to a great degree, we are putting ourselves, biases, emotional states, etc into the message the other person is "sending". It's pretty automatic. As a result we miss important parts of the emotional person's message, as we "tint", or mentally and automatically "spin" what the person is saying.
We all subjective beings, and this is normal, but it's not always productive (sometimes it is).
Synomyms: literal hearing, stripping "ME" from the equation, no self listening.
When we combine "us" with the speaker, it's sometimes hard to distinguish what the person means, from what we've interpreted the person means. It all sounds a little zen like, and in fact it is.
Literal listening involves mentally focusing on the words - the literal words, being said by the other person, and is typified by what is REMOVED.
The idea is not to THINK, INTERPRET, RE-CAST or TINT what is being said. We want to hear the other person, not the reflection of the other person in our minds.
Applying It To Angry Customers
This is a hugely hard skill to master, which is one reason why I don't teach it in seminars. Still, when dealing with an angry customer try as best you can to empty your mind of thoughts. Don't construct your response while the other is thinking. Don't go "into your head" with thinking".
Just BE there in the moment, taking in what the person is saying.
It's really a form of mindfulness, of being in the moment, the physical moment, without at least at that moment, feeling the need to DO something.