Do you want Egg on that?

There is a local bagel shop I like to go to and get what they call a eggwich and every time I place my order for an eggwich with ham and cheese they always ask me EGG, ham and cheese?  I always say yes, but I wonder has anyone ever ordered an eggwich and requested not to have the egg on it?  Wouldn't that just be a bagel with ham and cheese? and why would you order an eggwich if you don't want the egg?  Them asking me about the egg on the bagel is like asking when you ordered a hamburger if you wanted the hamburger meat on the burger.  Does anyone else find this question to be strange or is it just me?