If an alert client ask the caregiver to leave what should you do?

I assume that by "alert" you mean that the client has no dementia, and has the ability to make his/her own decisions. If that is the case, then asking a caregiver to leave is the same as asking anyone to leave your personal space. Also, the reason for asking the caregiver to leave is not given. Was the client uncomfortable in some way with that person? Was the client not feeling well and did not want anyone around? Did someone else set up the service against the client's wishes?

Most home care services come with a contract and a plan of care. That contract usually states that charges for the scheduled care will be levied if service is not cancelled by some time frame prior to services. So, asking a caregiver to leave still would cost the client the charges for a full shift that was previously scheduled. That, in itself, should be enough reason NOT to ask the caregiver to leave. However, if a client is alert, mentally competent, and able to make his/her own decisions, then, if a caregiver is asked to leave, the first step would be to politely state that certainly the caregiver will leave, as requested. However, the agency or the family, or whoever is also participating in the care, needs to be notified prior to leaving, that the caregiver is leaving the premises, so others are not surprised that the client is alone when others think he/she has care.

The next step is to determine what the care needs actually are, and how can they be met. Go back to my original extended questions as to WHY the caregiver is being asked to leave. If the client is uncomfortable with that specific caregiver, then a replacement can be sought. If the client is not feeling well and wants to be alone, then perhaps some medical attention is needed. If the care is being forced upon the client, then some other options for care need to be sought.