Open the order in Shopify admin and scroll to the Metafields section. The gift message is the field named Tacey gift message. It is kept separate from the order's Notes on purpose, so a gift message meant for the recipient never gets mixed up with delivery instructions meant for you.
Step by step
In Shopify admin, open Orders and click the order.
Scroll down to Metafields.
Find Tacey gift message. The customer's message is its value.
You can also see it in Tacey: open the order and look at its history, where it appears as Note or gift message added, labelled Gift message.
Why it is not pinned at the top of the order
Shopify lets you pin your own order fields so they show at the top of the order page. But Shopify does not allow a field that belongs to an app, like Tacey's gift message, to be pinned. This is a permanent Shopify rule, not a setting on either side. So the Tacey gift message will always sit in the Metafields section rather than at the top.
The easiest fix: use your own gift field instead
If you already have your own order field for gift notes (for example a "Gift wrap note" metafield you created), you can have customers write straight into it:
In Tacey, open Editing Tools, then Order notes & gift messages, then Configure.
Under Order fields customers can see or edit, pick your gift field.
Turn on Customers can see this and Customers can edit this.
Untick Let customers add a gift message, so customers are not offered two boxes that do the same job.
Click Save.
Because the field is yours, you can pin it, and every new gift message shows at the top of the order. See Should I use Tacey's gift message box or my own gift note field? for the trade-offs.
Things to know
A new gift message replaces the old one. If the customer adds a gift message twice, the field holds the latest one. The order's history in Tacey keeps both.
You can edit it yourself. The Tacey gift message field is editable by you in Shopify admin if you need to correct a typo before printing.
It is removed if you uninstall Tacey. Shopify removes app-owned fields when the app is uninstalled. If you want gift messages to outlive the app, use your own field as above.
What this does NOT do
Tacey does not email you when a gift message is left. Check the Metafields section, or the order's history in Tacey.
Tacey does not tag the order when a gift message is left.
Frequently asked
A customer says they left a gift message but the Notes field is empty.
That is expected. Gift messages never go in Notes. Check Metafields, then Tacey gift message.
I switched to my own field. Where are the older messages?
Messages left before you switched stay in the Tacey gift message field. New ones go to your field.
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