I just hit this after finding out Captcha was causing grief for prospective clients. In General -> Security I have captcha set to 'off when logged in'
I tried the tpl edits that Viggit posted above and whilst they remove the capture from the domainchecker page, they also make the domain checker not do it's job! With the code above removed, you can enter a domain into the input field, click check availability and it appears to go off and check it... but then when it's returned there's no availability shown - just the price table magically appearing.
What am I missing, or are the instructions above wrong?
At the moment I've had to set captcha to 'always off' but I'd prefer to not have to do this!