How do I return or refund gift money received through Zelle?

If you received money through Zelle, your bank is a part of the Zelle agreement and network, and they are using the email or phone number they have from you to identify you as the receiver. The sender definitely has entered your email address or your phone number to send to you - it doesn't work any other way. There are no account numbers or even bank names exchanged - the sender can only use email or phone number, and he will never know which bank you are with.

This implies that your bank supports Zelle. You might not know, or if you don't use online banking, you might not have access to it, but they do support it, or it wouldn't have ever worked.

There is no direct 'returning' or 'rejecting', all Zelle transactions are final. But you can send money to the original sender simply by doing the same thing the sender did: log on to your online banking, enter the recipient's email or phone number, and send it.
If you don't have their email nor their phone number, you can ask them, but otherwise, you are stuck.
If you don't use online banking, you can either start using it (it's nearly always free), or walk into your bank, and ask them to do it for you (I never tried that, but I'd think they can do that).