I used to approach use case diagrams in a, say holistic way; so every stackholder/party should be included.
And the customer <-> system interaction seems like a system use case - maybe you should enhance your diagramm with some verbs:
A system use case is normally described at the system functionality level (for example, create voucher) and specifies the function or the service that the system provides for the user. A system use case will describe what the actor achieves interacting with the system. For this reason it is recommended that a system use case specification begin with a verb (e.g., create voucher, select payments, exclude payment, cancel voucher). Generally, the actor could be a human user or another system interacting with the system being defined.
Source: Article on Use Case
PS: Use case diagrams are kind of high-level and appear in the start of a software development process. Other, more fine grained artifacts will emerge along the way.
PPS: And in the end, users are often (kind-of) ignored in traditional development models, so i think its never bad to sketch them on at least one diagram ...