The answer to situations like this is always to flag. Flag the offensive comment as "rude or offensive". And that's it.
Similarly, if the comments are specifically made in chat, you can also flag those.
After that, just walk away. Don't comment back. Don't try to reasons with someone leaving offensive comments. It's pointless. Just let moderators deal with it if there is a need to do so.
Should you find that your comment flags have little effect over an extended period of time, then you could perhaps go for a more extensive flag, i.e. the "other" option, and provide a custom explanation of what is going on. But give the situation some time to resolve itself before you do so.