Removing the thread is unnecessary. However, if you really want to do it, you should be able to do it yourself. Just hover over your very first message and a button saying "more" should appear in the lower-right of the message box. Click that and there should be an option "Remove". Click that option and it will close this thread.
Yes. Although saying it is "like deleting" is not quite accurate either. The difference between removing and closing is that, when removed, the thread won't appear on the board anymore. However, it is still accessible via contributions and other links; so it isn't quite like deleting the thread either.
The "like" is important in this case... because all the other stuff won't matter to most people. Also I'm pretty sure any links to a removed thread won't allow you to see anything... just that there were contributions and maybe replies, but they will be hidden which makes the links pretty useless.