I'm pretty sure the Mute function prevents alerts from members you've muted, so you won't be notified when they post in a thread you're tracking. But I don't think there's an "ignore" where the posts are actually invisible to you. Just doesn't seem to be a current feature of this system.
If it's an issue of someone trolling a thread, you can flag the post and a Mod/Admin will double-check what's going on. But if it's an issue of being annoyed with what someone wrote, skimming over it is the best bet. (Difficult to do in PWI, I'm sure.)
I think that may just be based on the thread title that's being typed, similar to a Google Autofill.