The restaurant's original menu featured over sixty dishes, many of which sold only a handful of times per month. ______, the owners cut…

The passage describes a problem, an overly large, inefficient menu, followed by an action taken specifically to address it, a deliberate reduction. In response correctly frames the menu cut as a reaction to the problem just described. Regardless would suggest the change happened without regard to the described problem, but the passage frames the cut as a direct answer to it. For example would present the second sentence as an illustration of the first's claim, not a response to a stated problem. Namely introduces a specific instance of something just named, which doesn't fit this cause-and-response relationship.