You just make sure the client is aware of the distinctions:
Email is more inherently optimistic, and it's more inherently asynchronous. When the client sends a message, it assumes the recipient receives and processes it. Failures aren't necessarily reported. And those failures that are reported aren't always even reported back to the sender. And they sometimes can't be -- like if the sender uses a black-hole
On the contrary, because HTTP is designed for document fetching, API's that run over HTTP can and generally do respond immediately with detailed success codes and messages directly to client. And while asynchronous message processing is still an option here, it's much more in-line with HTTP for clients to receive immediate success/fail operations if those are needed.
There may be other important things to point out. One of those might be, "I can develop REST API's faster, b/c it's what I normally do." And those points aren't invalid. But, they're not technical reasons. They're practical realities.
But, that's basically it. If you're competent enough to work it either way, you mostly just need to decide with the client whether the integration needs immediate failure processing, or whether the client-machine(s) can safely ignore errors.