Modifying Voltage Controled Amplifier to become attenuator
Put an attenuation stage after the VCA. Then your gain will range from the attenuation factor (when the VCA is at unity) to the attenuation factor times the VCA max gain (when the VCA is at max gain).

A simple voltage divider and op-amp buffer will probably suffice for most applications.

However, this solution has a bound on maximum attenuation (i.e. you cannot have an infinite amount of attenuation (gain = 0), which may or may not be appropriate for your application.



Or you could find a different circuit entirely, because I don't understand why you have to modify that circuit instead of using a completely different circuit.