Can I turn off the Shopify New Gift Card email notifications when connecting customer accounts?

Unfortunately, there is no way to turn off these notifications if you link a customer's email or phone number to a gift card. These notifications are sent directly by Shopify, not through the app.

However, you can import the gift cards without adding the customer's email or phone number, and in this case, no notification will be sent out. This is the route most merchants take for a seamless transition, especially if the customers have already received their gift card information from a previous system or in person. You've got to remember that we are importing the exact same Gift Card Code from the previous system. So whether they have a physical card or an email/SMS from the old system when they first got their Gift Card. That method of delivery still exists!

If you absolutely need to link the gift cards to customer accounts and want to avoid confusion, you might consider sending a bulk email in advance (to all of the customers that have Gift Cards) to inform them about the upcoming notifications and to disregard them if they already have their gift card information.