Congruent feedback refers to the content, focus and words used in feedback. When feedback is congruent, the given information is directly related to what a person has asked for. It may be useful or not useful, it may be what the other wishes to hear or not, but it is directly related to the question or request. In-congruent feedback, on the other hand, can give information that may be important, but is either not related to the focus, or adds another focus. Some examples:
In-congruent feedback and information does not have much to do with learning how to communicate better, nor with applying some formulated sentences that do not sound authentic, nor with how to lower barriers (of others). The words necessary for congruent responses are (usually) already in the givers' vocabulary and can come out of mouths (or keyboards) authentically once one puts oneself in the shoes of the receiver of the information. In short, it has to do with a lack of empathy, and often also with (perceived) power plays. But what will there be first, the chicken or the egg? One can practice empathy by thinking first, and considering self, other and context before producing feedback (or meta-communication).
Meta-communication (communication about the communication) is the key out of all of these situations. In the case of a true double bind, a third person may be required, but meta-communication is still the key. Something like, “What can you say to me right now that your intonation, body language and facial expression will agree with?”, or just leaving the field as a form of meta-communication (in which case it wasn't a true double bind).