This sounds like a good time to speak with said person in private either through a private message or alternative communications.
I typically use this approach to community influencers who I don't want to moderate in public, but also need to get them back on track to following the guidelines. Speaking with them in private adds a personal touch where can both talk about the issues. The outcome is mostly favorable because we can get it all out and the open and resolved.
This approach may work best for you because it's in private and not on the forums where you have to worry about things becoming less formal.
Remember, even if you're speaking to someone privately, only communicate what you would communicate to everyone in a public channel. Assume that everyone in your community is listening in on your private conversation and never assume that you will never be quoted, because you will eventually.
If you take the approach of speaking privately with a user about his or her conduct in your community, then you may see a retaliation from the specific user in your community or other communities. That retaliation will normally include either a direct quote from the conversation, negativity on the conversation or just pure slander on the representative themselves.
(Note: This is why many community guidelines and rules entail not to repost moderated material in the public forums. Consider adjusting your own guidelines to reflect this.)
Retaliations like these can occur regardless of the communication platform. It can occur because you moderated a user in a public forum or because you spoke to them privately.
When actions like these happen on your channel or forum, the best course of action is to remove the comments. Although I personally rarely delete/remove comments, this is one of the few cases that I do simply because it normally include private dialog that is not for the public forum or channel.
When removal happens, a private message should be given to the user with a clear explanation on why it was moderated and what course of action needs to happen next. If it continues, the last resort if you can not come to a civil resolution via private communication is temporary suspension or permanent banning.
When it occurs in another channel or forum that you do not control, then there is most likely nothing you can do in terms of moderation unless you know someone on that channel. The best course of action there is to avoid being pulled into the discussion right away. Relax, see how it develops and know that majority of the users on your channel are likely not viewing the communication on another channel.
If you notice that the thread is developing into something bad, then engaging the post may be recommended AT caution. The reason caution is highlighted is because you are entering a channel you have no control. When you have no control, the wrong things can be happened or said.
That's why it's important to be patient, watch the discussion and plan out your response while considering the impact of said post after it's been published. Sometimes the best approach is simply explaining your side of the story and then letting it drop. Others have gone deeper down the rabbit hole and engaged in deeper arguments. But, going deeper increases the risk of both making you look bad, the organization look bad and possible setting yourself up for failure.
Consider the risk versus reward and engage at your own risk.
Address The Issue
However, if you choose not to address the issue, then it will continue to happen or worse, fester into something that forces your hand to do something else. Either way, address the issue, get the user back on track and everyone is happy (hopefully).