FWIW, Pokeweed is a very persistent, long-lived perennial that readily seeds itself (and is readily seeded by bird poop - they love the berries.) It quickly develops a deep taproot that can become absolutely massive. I strongly recommend digging out seedlings as soon as you recognize them. And dig them out - don't pull. It may take a year or so, depending how deep any broken off roots are in the ground, but any broken-off tips of roots will resprout.