CF7 Form fails if webhook is 405

We ran into an issue where a service provider of an API where we send leads was down and the URL of the webhook was returning a 405 message. This made CF7 fail to send mail and fail to redirect to a thank you page that another plugin makes possible.

Is there any way to fix this issue so that the response from the webhook URL won’t break the form on the frontend if there’s a 405 error?