the only personal information a log contains is the directory of your honorbuddy installation if (and only if) you safed your honorbuddy on your desktop
and uses your name as username.
c:\user\Max_Mustermann\Desktop\Honorbuddy
@Shyoden:
to delete the logs within the board go to
"settings" (between my_profile and logout)
and then to Miscellaneous -> Attachments
and there you can delete the files