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Solution
When the local payment method deletion ( https://apidocs.chargebee.com/docs/api/payment_sources?prod_cat_ver=2#local_delete_a_payment_source) is done, the payment method is deleted from Chargebee but remains in the gateway.
When the payment method is permanently deleted (https://apidocs.chargebee.com/docs/api/payment_sources#delete_a_payment_source), it is deleted from the gateway as well.
However, in case of GoCardless direct debit, the payment method doesn't get instantly deleted from the gateway even if the permanent deletion is performed. The payment method becomes inactive.
This is because GoCardless is keeping the payment method inactive to maintain the payment history against the mandate which is meaningful. If the merchant wishes to remove the mandate completely, they can delete the inactive customers in the GoCardless dashboard as suggested by the GoCardless team.
Currently, Gocardless does not have an API to delete the mandate. Hence, Chargebee will not be able to modify the integration to suit that. Inactive customers can be removed from the GoCardless dashboard altogether, to permanently delete their payment/mandate history and all associated personal details. To make a customer inactive the merchant will first need to cancel their customer record. Once this has been done, they can follow the steps below.