We're told by traditional merchant banks (not Stripe) that they will dramatically lower your credit card processing rate if you ask customers for their zip code.
That being the case, by default we ask customers for their billing zip code and send this to your merchant bank.
Even if this is turned on, we generally don't use AVS to check that the zip code matches what's on the card, because instances of fraud in Starboard Suite are close to 0, and AVS checks may create problems for international cards.
We do have the ability to enable AVS checks against the zip code, but doing so may cause increased customer frustration, so it's not recommended unless you're experiencing fraud, or if your merchant bank requires it. If you'd like to add an AVS check, please let us know.
If, after reading this, you'd still prefer not to collect customer zip codes for some reason, you can disable this by updating the setting called "Collect Customer Payment Zip" in Admin->System Configuration.