As you say, back to the beginning .... although I'm a little confused as originally your post suggested the complaint had been upheld and now you're saying the clerk was exonerated. So, in general terms it looks as if there was a complaint, dealt with in accordance with your complaints policy. This seems to have been accepted by the majority when presented to the council but a few disagreed with the result and wanted their disagreement recorded. It is now suggested that the letter sent as a result of the complaint (presumably in accordance with your complaints policy) has not been sent.
Firstly, people don't always agree with the majority. It's called democracy. The council is a corporate body and the majority vote is the decision. Sorry, but that's life. Whether the group wanted their vote recorded (and to do so you need to ask for a recorded vote before it is taken) is irrelevant as the majority vote prevails.
Secondly, the letter wasn't sent. Not clear why that would be but given that the original complaint was about the clerk, personally I'd suggest the chair be authorised to sign the letter on behalf of the council in this instance. This is not a legal requirement but seems appropriate under the circumstances.