Hello Dave

This is hairy bittercress, Cardamine hirsuta.

The beat time to pull this weed is before it has set seeds. As you found, the seeds disperse easily once they are present.

There are weed killers labeled for lawns that manage this weed. See a list of active ingredients here-

https://extension.psu.edu/lawn-and-turfgrass-weeds-hairy-bittercress

In lawns keep flower heads mowed off and bagged to minimize more weed seeds from being deposited. Mow when the weed is still flowering.

Hairy bittercress is a winter annual weed. Its seeds germinate in fall beginning as early as September. This coming late summer to early fall apply a pre-emergent (listed above) to the lawn to prevent the seeds already present in your soil from germinating. Note that pre-emergents prevent all seeds from germinating, including grass seed.

You may want to apply a pre-emergent labeled for garden beds to prevent the seeds from germinating there, too.(Preen labeled for flower beds is one example, there are other brands).

Please read and follow all label directions and precautions. Do not apply anything to edible plants unless it is labeled for that use.

Here is additional information from MSU Extension

https://www.canr.msu.edu/news/hairy_bittercress_a_weed_to_watch_out_for