is there any way I can deactivate the WPML / Deeply "Automatic Translation" API that you can see attached, after I did all translations? I just want to avoid that the client uses our WPML credits from now in in the future
You can disable "Paying-As-You-Go" from WPML > Translation Management and click the Tools tab. In the Pay-as-you-go account details section, click the "Stop using pay-as-you-go" link.
The next time the client will sign up, the plugin will ask for new credit card information because WPML does not store them.