It's a bug that mark old messages as new. Facebook already experienced such issue in the past. Did you try archiving the chat to see if that prevents it from reappearing? You can also report this bug to Facebook by selecting your profile in the top right > Help & support > Report a problem.
I've checked my support inbox & there's no record of me messaging fb help at the start of this week about this problem so I submitted it again but still no record shows in my inbox unfortunately.
I don't think I'll be holding my breath.
Update if anyone with the same problem was wondering how this turned out for me, drumroll:
Absolutely nothing as I predicted. No response whatsoever from fb & no records of me submitting this problem to them twice.
Looks like I'm just stuck with this anomaly, oh joy.
Sorry to hear that the issue is still not resolved...
I have another suggestion. Log out of your account on all your devices. Clear the cache of your browsers and also on the Facebook apps (uninstall and reinstall the app to clear the cache on your iPhone).
Next, log in to the Facebook website only on your computer. Delete that chat and make sure to select the option to delete it permanently.
Log out and log back in. If the chat doesn't reappear, you can log in on another device and see if that chat is really gone forever. If not, repeat the steps once again and try deleting (for yourself) all messages in the chat before deleting it completely.
Let me know how it goes.