Actually, it can be edited. When you click on CONTACTS TAB > CLIENT NAME > "Client Log" tab and choose the date range so that the client log post you want to is being displayed, then you'll find an "Edit" command in the drop-down list to the right of the Client Log entry. Click on that and you'll be able to edit the content. And just below the content editor where you type your text you'll see the option "Show log to client". Click on this to uncheck it and when you click "Save" this post will no longer be available to your client. Also, if you previously attached a document/file to the Client Log message, you have the option to delete it by clicking the little red button ( [x] ) at the right at the Note Files.
Something to keep in mind though: If you originally chose the option to "Show log to client" AND you also chose to "Send email notification to client" and "Include log note in email", then the client would have received an email with the content of the post and the attachments included in the email message. If later you change the post to NOT display for the client, your client won't be able to see the post when they log in to their private website, but if they still have the original email, they'll have the message and its attachments.