you can follow this steps -

To disable or adjust the automatic message that asks users for their email in Intercom, go to Messenger Settings and locate the option “Require an email for starting a new conversation.” Here, you can customize when and if this prompt appears, such as only outside business hours or not at all, which can help you manage initial interactions more flexibly.

For detailed steps, check the Intercom community discussion on this topic here

Hi, I did not find that setting. I managed to turn the email off: go to Automation > Basics > For leads > Ask for contact details and disable it there.