Open the thread in question that’s bugging you. Look all the way at the top or the bottom to see if it says "Notify" or "Unnotify" (this is on the green band that says "Reply Notify Mark Unread Send This Topic Print"). If it says "Unnotify," click or tap that and it should solve the problem.
I obviously don’t know whether you ever use Tapatalk to access the forum, but if you do, take note that when you reply to a thread, that app will automatically subscribe you. In the app, there is an icon that looks like a bookmark at the top right corner when you view the thread. If the icon is solid, it means you’re subscribed (tap it to unsubscribe); if the icon is an outline, it means you’re unsubscribed. I mention this because this Tapatalk "feature" can be unexpected and annoying.