We have the message warning customers that the call is being recorded at the beginning of all our calls. Is it possible to remove the message at the beginning of outgoing calls only, but keep it for incoming calls?
Are you recording outgoing calls? If so, I believe legally you have to state that you. are.
If you are not (there is a setting under Account Mgmt->Account Settings->Zoom Phone where you can specify which calls to record. Inbound, Outbound or Both. You must have Admin privileges to change (or view) this setting.
I'm not providing legal advice here... just information.
In the US, there are some states that require two-party notification, meaning that both parties (and in most cases ALL parties) need to know that a call is being recorded. Other states are one-party notification states, meaning that only one person on the call needs to know the call is being recorded -- which is typically the caller.
Seek legal advice on the laws in your state and/or country.