Kyle,
I have a black lab mix puppy that loves to pull up grass and other plants, but mine eats it, roots and all. He also likes to dig and if he can't pull a plant out with his teeth, he'll dig it out. I don't leave the dog out alone for very long, and he's learning that I really don't like it when he pulls up plants from the flower bed.
Have you tried spraying sour apple spray or something similiar on the plants? It sounds like he's going after a specific plant. So you could spray just that border grass. And you could also work on catching him in the act and spraying him with water from a spray bottle, or a vehement 'no'.
Of course, my pup likes water and thinks the spray bottle is a fun game. You don't say how old your lab is, but make sure he has chew toys with him if he is outside while you're gone.
Have you tried a Kong with treats frozen into it (peanut butter and kibble)? It is an appropriate item to chew, and will keep him occupied for awhile. And delay boredom, which can lead to destruction.
Good Luck
