Thanks for your question.

Just to be sure that we are dealing with the correct weed (it goes by various names including those that you mentioned as well as snow-on-the-mountain), check out the following:

https://www.minnesotawildflowers.info/flower/goutweed

https://www.invasive.org/weedcd/pdfs/wgw/goutweed.pdf

There are essentially three ways of controlling this weed:

1). A process called solarization. This essentially consists of laying a tarp over the plant so as to cut out sunlight. This is a slow process (at least 2 to 3 weeks) and is sometimes effective and sometimes not.

2). Digging it out by hand. This is very labor intensive and often it is difficult to remove all the roots. The plant continues to come back.

3). Use of herbicides. Often this falls into two different categories. Broad leaf herbicides containing as active ingredients 2,4-D, MCPP, MCPA, dicamba, and/or triclopyr. This group of herbicides is taken up by the leaves and is claimed to be broken down within 72 to 96 hours after application. Secondly there is group of herbicides that is taken up by the leaves and stems and transported to the roots. This group is an example of a systemic herbicide meaning that it enters into the entire transport system of the plant. It can be extremely effective. However it can persist in the soil for several weeks and thus prolong the time period that one must wait before planting something else. Additionally, this group of herbicides is very detrimental to most pollinators. An example of this group is glyphosate (“Round Up”).

As you can see there is no easy or simple way to eliminate this weed. Once established, it is almost impossible to eradicate it completely. For your case, you might consider a couple of applications of a broad leaf herbicide over a two week period. It would be best to do this ASAP while the weed is actively growing. Be sure to read the label on the herbicide regarding when one can plant following application. After this herbicide treatment but before planting try to dig it up as completely as possible. Don’t be surprised it reappears later in the season. See also the following:

https://www.gardeningchannel.com/how-to-get-rid-of-invasive-bishops-weed-goutweed/

http://www.ecosystemgardening.com/kill-the-bishops-weed.html

https://www.gardeningknowhow.com/ornamental/groundcover/snow-on-the-mountain/snow-on-the-mountain-plant.htm - :~:text=Snow on the mountain plant only responds to herbicides when,see a solid green plant.

As mentioned, completely eliminating this weed will take considerable effort, a high level of persistence, and great resolve. Good Luck!!