If you don't want the gifting option available, you can remove the "Give a Gift" link from your theme, but the "This is a gift" option will still be available on your checkout page. You can hide it using CSS, but it can still be set to checked if subscribers are following cached links from search engines. The most effective way of stopping gift checkouts is to use Javascript to fully remove the section from your checkout page.
1. In Code Editor, open components/checkout/Checkout.
2. If you do not already have a file named component.js, then click "+ Add New" and create a filename called component.js and click Save.
3. Open up component.js and in it, add the following:
<script>
$( document ).ready( function(){
$("#gift-form").remove()
});
</script>4. Click save.
This will hide the gift options from your page on checkout!