You can kick people from your guild, but beware.
Once you let someone in your guild, they acquire your guild channel. Then if you kick them some time later (for whatever reason) they can still see your channel on the chat client, and talk on it.
Lessons to be learned:
-No org channel is secure (I'm sure theres a way for people to get to your channel without ever being invited as well)
-Troublesome people can continue to bother your guild, sure you all can ignore them, but everyone has to do it themselves.
-Create/Use some form of a chat bot that works on invite only and can kick/ban people from the channel.
Possible problems:
-It may be possible for people to snoop on bot channels as well, meaning no ingame communication is "safe", except direct tells.
-Any GM/Ark channels may not be safe either! I don't actually know if they have any that they use, but I suspect they do.