how can trust be given if there is no transaction?
Trust is not inherently tied to a transaction. Trust can be given for any reason. While a trade is what is most obviously something that warrants trust (or mistrust), people can do other things too that warrant trust. Furthermore, the forum has no idea of whether a transaction took place, and it is difficult for moderators to verify that.
The person who added that trust feedback is not responding and ignored our messages.
They aren't obligated to respond to you, nor are the moderators.
This is definitely supposed to be a moderator issue, if it relates to allegedly breaking some forum rules and has nothing to do with the member who left the feedback!
It is not a moderator issue, the trust does not break any forum rules. Some people like to also give negative trust to people who they believe to break forum rules, in addition to reporting the user to moderators. They are allowed to do that.