As Tokyo Nagoya pointed out, the phrase was parsed incorrectly. The correct division is:
「お[客様]{きゃくさま}の[声]{こえ}」 + 「[室]{しつ}」
However, regarding translation, it seems that "Customer Service" is a little off since 「お客様相談室」 is a more appropriate term for it, as Chocolate mentioned. Recently, I realized that the phrase may actually be a very literal translation of 「お客様の声」
from the business concept Voice of the Customer
.
From Wiki
"...a market research technique that produces a detailed set of
customer wants and needs..."
Using this, I found a localized site from the same company that was used in the context of the question. The term Customer Voice
was used.
So, to summarize, 「お客様の声室」
or Customer Voice is a service that serves as an outlet so that feedback— the customer's thoughts and opinions— may be heard.