I would not use 'ease' in this situation. The verb 'ease' collocates with 'pain' or 'discomfort', so it tends to be used in a medical or caring context. I don't think it works in a business context, and I don't think that 'ease' collocates with 'emotion' or 'anger'.
When speaking to a colleague, I might talk about 'placating' the customer as a formal term, or informally (and off the record!) I might say 'calm her down'.