The template in question is
vendor/magento/module-sales-rule/view/frontend/web/template/payment/discount.html
and it shows at the checkout
The rule that places the template in
vendor/magento/module-sales-rule/view/frontend/layout/checkout_index_index.xml
is
<item name="component" xsi:type="string">Magento_SalesRule/js/view/payment/discount</item>
It can be done by disabling the component in an overriding XML file.
app/design/frontend/Vendorname/ThemeName/Magento_SalesRule/layout/checkout_index_index.xml
<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<body>
<referenceBlock name="checkout.root">
<arguments>
<argument name="jsLayout" xsi:type="array">
<item name="components" xsi:type="array">
<item name="checkout" xsi:type="array">
<item name="children" xsi:type="array">
<item name="steps" xsi:type="array">
<item name="children" xsi:type="array">
<item name="billing-step" xsi:type="array">
<item name="component" xsi:type="string">uiComponent</item>
<item name="children" xsi:type="array">
<item name="payment" xsi:type="array">
<item name="children" xsi:type="array">
<item name="afterMethods" xsi:type="array">
<item name="children" xsi:type="array">
<item name="discount" xsi:type="array">
<item name="component" xsi:type="string">Magento_SalesRule/js/view/payment/discount</item>
<item name="config" xsi:type="array">
<item name="componentDisabled" xsi:type="boolean">true</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</item>
</argument>
</arguments>
</referenceBlock>
</body>
</page>
