Liquid Metal Thermal "Thermal Grease" on a Peltier Element?
There are soft metals (indium, for instance) that make good thermal
gaskets, but for a Peltier module with a flat ceramic pad,
a flat heatsink just needs a very thin layer of some grease to
make good thermal contact.   The flatter the heatsink, the thinner
the grease layer.   Unless the ceramic has extremely high thermal
conductivity, the thermal resistance of the series ceramic-grease-metal thermal path is not dominated by the grease.

So, the answer is yes, the thermal conductivity of the 'grease' matters.  But it doesn't matter much.