@dalehileman,
The red NEW is for posts you haven't looked at yet, but if you don't refresh the page, you'll still see the red new. You can go to the New Posts page, and get rid of all the reds you have looked at by refreshing the whole new posts page (not just the immediate page the post is on).
I just caught on - you want to erase the post since you read it? Or merely get red of the red NEW?
THREADS - if you don't want to see them or are finished reading the thread and don't want to see it again, then thumb down. Most of us do that easily with subject matter we are not at all interested in; it's a kind of housekeeping.
POSTS ON THREADS - if you don't want to see someone's post, down thumb it, or put the person on ignore. Most of us let stuff that we don't like go, or we'd be down thumbing way too much and it can be kind of mean. If you've already read it and are fine with it, just refresh the page and the red New will go away.
Some of us try hard not to downthumb posts, and do that relatively rarely, resorting to discussion or arguing, just letting it go, or resorting to ignore. On the other hand, rewarding interesting posts with a thumb up is a friendlier move.