It sounds like I jumped into the middle of a conversation, so not sure if this will help.
If you have old inquiries in your Inbox that you don't want to appear anymore, simply archive them. Move the mouse to the row where the message is an on the right side, you will see an archive link. You can always go back to your archive folder if you need to look up an old inquiry. If it's simply an inquiry, as long as you've responded you don't necessarily have to decline.