In this documentation, we can check how to manage gift messages in Magento.
1) Login to Magento admin panel.
2) Go to ‘Catalog’.
3) Click the option ‘Manage Products’.
4) Select the product name and click the ‘Edit’ button.
5) Click the option ‘Gift Options’ in the left menu panel.
6) Select the option from drop-down menu ‘Allow Gift Message’.
7) Click the button ‘Save’.
That is how we can manage gift messages in Magento.
If you need any further help please reach our support department.