A moist warm compress or heated eye mask functions with the same underlying principle as TearCare:
Heating the lids to liquify any clogged oil
Clearing out obstructions in the meibomian glands
Though they target the meibomian gland dysfunction (MGD) root cause of dry eye and provide relief, they are less effective on both counts due to:
Inability to reach measurable therapeutic temperature of 41-45°C (105.8-113°F) to melt meibum since each microwave has non-uniform power levels and timer settings
Inability to maintain consistent therapeutic temperature for at least 10 minutes.  You constantly have to reheat the warm compress every few minutes as it cools off very quickly
Less than optimal contact between the warm compress and eyelids
Difficulty for you to effectively express the meibomian glands through lid massage with your fingers.  Most people forget and don't do the finger lid massage after using the warm compress.
In addition, squeezing meibomian glands with your fingers is like squeezing toothpaste out of tube on a pillow.  The back of your eyelids is your eye, which is soft tissue (like the pillow).  Anything you manage to squeeze out won't come out easily.
During your TearCare treatment, our eye doctor uses forceps (a flat tweezer-like surgical instrument) to provide equal pressure on both sides of your meibomian glands to unclog them.  Think of it as squeezing toothpaste out of a tube while placing it on a hard tabletop or counter.  It is much easier and faster!