This is an obnoxious plant. It is a relative of the ornamental geranium but is the sibling that misbehaves. Once you get it in the garden, it is very difficult to get rid of.
It is also known as Carolina Geranium and as cransesbill and officially as Geranium carolinianum. The leaves are kind of pretty, but they intend to invariably grow where you don’t want them. Frequently right next to things you do want.
If you can, pull the new ones before they get established in the spring. The reason is that more established plants put our runners or long tuberous roots that can go for two feet or more.
Also, deadhead them so they don’t put out a lot of new seeds for the following year.
Even weedkillers like roundup don’t seem to do much. It may kill the plant on the surface, but unlike so many where it kills the roots as well, it doesn’t seem to get far in the tuberous roots and the plant just pops back up someplace else. One person suggested several treatments in a row of Roundup.
Apparently the plant is an annual, so the plants in the spring are from seeds and not coming back from the prior year. I have also seen that it is a biennial where it grows one year and the next flowers, goes to seed and dies.
If that is true, then even though it puts out the tuberous roots, they should die off, so if you are diligent over a period of two years, you should have the problem licked.
Putting down something like Preen to prevent germination of seeds should be a major help in controlling the weed. If you want to try a more natural way, corn gluten meal spread over the ground should also do the trick.
It is important to keep up with the treatments because the seed has hard membrane which can survive a long dormancy in the ground.