Right now, the puddles are short "river" overlay elements, that stands out as a bug, when someone digs them up, showing the rectangle of water surface floating in the air.
Instead of deleting all puddles or making the area around them undiggable, i suggest the "river" elements be replaced with dynamic elements that has a simple "seeping into the ground" animation, that has the "destroy" hitmesh around the puddle. That way the player can start to dig up the puddle, destroys the hitmesh and the water seeps into the ground, instead of being a buggy plane of water or a unrealistic concrete bowl buried in the ground.