"The team believes Mars must still be geothermically active"
Mars is tectonically dead. It has no magnetic field, which means its core is not moving any more.
Granted, the sheer volume of material is going to take an undetermined amount of time to cool off, but if the core was that hot, the ice would have melted.
There may well be a point below the surface where the core can agreeably heat an underground dwelling, but I fail to see how that can impact subsurface ice.
Of course, I'm not a geologist, much less an exo-geologist, so maybe I'm just ranting for nothing.