If left unpulled, stands of garlic mustard will become denser year by year, releasing toxins into the soil that inhibit the growth of other plants (can you say "allelopathic"?). If you have a patch that feels overwhelming, here's a success story to inspire you.
It's best of course to nip an early invasion in the bud. In any given year, you'll see two generations of garlic mustard. In the first year of growth, a biennial plant only produces leaves, gathering energy to launch a flowering stem in the second year. I just pull the second year plants, ideally when they first appear in the spring, but usually when they are in bloom and easiest to spot.
Pulling time is in April, extending into May. This first bloom, in the photo, was on April 10, but they're still blooming now. The clusters of white flowers can make weeding feel like an easter egg hunt. Last year, we had a girlscout troop pull garlic mustard that was growing along the edges of the Herrontown Woods parking lot. They got every last one!
That's the strategy, to pull every last one, before the seeds mature and scatter. If this is done year after year, the soil will run out of seeds to sprout. Each year there will be fewer and fewer plants, as the seedbank in the soil becomes exhausted. How many tasks do you know that get easier every time you do them? It's important to get every plant, every year, so the seed bank can't rebound.
What to do with them once they are pulled? Some people stuff them in plastic garbage bags and put them out with the trash, but though that gets rid of the seeds, it also makes more trash. My strategy is to make a pile. Word has it that even if you pull them in the flowering stage, they can still develop mature seeds. So don't just leave the stems scattered around the yard. If you concentrate them in one pile, it doesn't matter if any seeds mature, because the new plants will all be in one spot and easy to pull or smother. It's important to locate the pile where heavy rains won't wash the seeds away from the piles.
We've been pulling garlic mustard and piling it like this for years around the Veblen House. This year, it took about an hour to get every last one and put them in this small pile, resting on a log, roots drying in the sun. That job's done for the year. It's a rare feeling for a gardener. I don't entirely trust it, and am going to go out again and check, just to make sure.