I am using the REST API to submit documents for InPerson signing from my website. When the documents are completed signing, Docusign inserts the EnvelopeID at the top of the
The "Envelope ID Stamp Control" feature in Preferences >> Features gives you the ability to set the Default ID stamp behavior (enable or disable) for Envelopes that are sent via the account. If you NEVER want ID stamped on any of the envelopes sent via the account, then click the "Envelope ID stamp control" link, select "Remove Stamps" and Save.
Additionally, even if the ID Stamp is enabled at the account level (i.e., "Stamp Pages" is selected in Preferences >> Features >> Envelope ID Stamp Control), you can still override this setting for each individual envelope you send. Via the REST API, you should be able to do so in the API request to Create the Envelope (POST /accounts/{accountId}/envelopes), by setting the envelopeIdStamping property to false -- to prevent the stamp from being added for the envelope being sent.