If you leave someone with a -ve rep and he/she does the same in retaliation, can the mods remove it?
The trust system isn't moderated the only way a red tag can be removed is by appealing with the user that tagged you to removed the tag. Although administrator can interval in some special (serious) cases and remove the tag if necessary when it's a false one.
Note: Not every negative feedback you get contributes to you trust score, some will be seen as "Untrusted feedback" depending on the viewers custom trust list settings.
To understand more visit thread below and read through this paragraph:
The moment you start leaving negative feedbacks on other users accounts, you'll make enemies and probably get false red tags so you have to read these quotes on how false negative feedback (red tags) can be handled