Last year I noticed a small patch of this stuff up against the house here--I pulled it up and hoped for the best. There was also a little on the far side of the small woods below the house--I haven't gotten in there yet to take a look. So I've been pulling out what I can. Garlic mustard has a good strong taproot, like a carrot or dandelion, and will break off it quite easily, and then quickly grow back. After some rain, I was getting more out by the roots, but a lot of it is inaccessible, and a lot of root is left in the ground. I've been dumping it in the compost, but I suspect that the stuff with root intact may succeed in producing seeds in spite of having been pulled up.
This powerful invasive was first brought to North America by European settlers for eating--but like so many that came this way, there were no natural controls on it here, so it spread terrifically. And then I read that it not only chokes out native spring flowers, but it also damages forests. (See this post from last spring at Bootstrap Analysis for more on this invasive and forests. See this page for what the Ontario government has to say. And a link to Wisconsin's Garlic Mustard Awareness Month I found at BirdFreak Blog)
The stuff seeds prodigiously, and the seeds can wait for years to sprout. Who knows what happened to this bit of earth I'm dealing with. Two patches occupy the exact same space as two clumps of daffodils--very suspicious, as if they've had some (inadvertent, I'm sure) human assistance to take hold. Other, larger patches are not in places where they would have been planted through the spreading of composted garden waste, or something like that--but maybe they're where torn up plants were tossed? I think I better pull the plants out of the compost and bag them up in black plastic trash bags and set them in the sun. Maybe cooking will prevent seed development.