Often I get requests like these from clients, asking to change a simple phrasing or way of handling certain requests. Unfortunately in my case, this client is one of our franchise locations and has their agent built on a template that if changed, changes the entire way the franchise agent operates for all locations.
Clearly, not telling customers you are closed is minuscule and has no real impact on the call, but they seem to think it does. We offer an additional "tier" of agent where offices can further customize agent responses for a premium over our standard "tier", so we could accommodate this if they paid for it. I'm just not sure how to respond to requests like these given our situation.