I don't know what your weed is, but I suspect it was in the lawn that was there and it spreads by runners or it's roots since I don't see it in the bed above.* Since it's blooming now I would suggest you get rid of it or cut it back immediately so it doesn't go to seed and spread to your other beds. It's best to pull weeds after a rain or a good watering when the soil is moist.* Try digging down to see what type of root system it has.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.