Consumer surplus from a Hicksian demand curve: what is it?

A Hicksian demand curve indicates how much of a good will be demanded given price holding level of overall utility fixed.

When in equilibrium with a supply curve we end up with this area we would call consumer surplus, however we can no longer interpret it as "income saved by the consumer with respect to his actual demand" which is an appropriate interpretation when marshallian demands are used.

How exactly do we interpret this type of consumer surplus?