If the Order status is “Complete” you should see the gift card number on the line item of the order.
As long as there is a gift card number, that means it has been generated and email was attempted to send.
First, check the Junk Mail folder for the recipient email address. If the gift card is not there, the email may have been sent but been outright rejected by the recipient’s email server (not even going to the Junk Mail folder). Most email servers are very strict when it comes to attempting to prevent spam and may see the Gift Card email as possibly junk mail. As a result, most WooCommerce installations are not trusted by default, since anyone could send out spam from their server.
To combat this, we recommend using Pepipost to handle your email delivery. There is no cost (until you send more than 3,000 emails in a single month and even then, it’s pretty inexpensive for the service you get). They will ensure that your emails are delivered and you can even track open rate to know for sure that someone received their email and opened it.
https://pepipost.com
Pepipost integrates into WordPress easily with the WP Mail SMTP plugin (also free): https://www.ads-software.com/plugins/wp-mail-smtp/
Also, we have recently been made aware that some website hosts deliberately block the wp_mail() function in an effort to prevent spam.
Contact your website host to see if they have anything in place that prevents outgoing email, specifically via the wp_mail() function.
If you don’t see the gift card number then make sure the order is Complete first.