Unfortunately JIRA Service Desk (nor JIRA itself) does not have any SPAM handling / filtering capabilities for their email integration. The system just grabs everything from your email server.
It would indeed be nice if they'd incorporate something, as most (if not all) good support systems to provide some level of SPAM filtering (we use Help Scout for some of our support, and they have a great filtering system), but as of now I'm afraid there is nothing.
You might try beefing up your SPAM handling at the server level, or see if your hosting provider or whomever handles your email server for you can help incorporate some level of SPAM blocking so they don't even land in your server.
The CAPTCHA reference here I think is in relation to the portal. All I can find on Service Desk filtering is through managing spam in your original email account settings.
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