Guardian Tears are dropped from Guardian 2, and very rarely from Beach Monsters and Guardian Trio loot bags [ confirmed ].
They are used to craft the Amulet of Healing Rain, which acts like a rain potion when equipped, however costs 25 of them to make.
When you have the Flexible logs Unlocked, using the amulate while cutting down normal trees yields Flexible logs or as refered to Flex Logs.