First, are you sure it's loosestrife.

Has it flowered? A few or single plants are not difficult to dispose of, particularly if have not flowered and set seed. Dig it up. Be careful to get the roots, and monitor the area for any shoots appearing from roots you may have missed - even though you will be very careful not to miss any. If you cannot burn - Put all plant pieces in plastic bags (vegetation rots quickly in plastic), leave them in the sun. When rotted, dispose of in your garbage.

Yes the larger one flowered quite a bit last year. I just thought it was a pretty bush. The small ones flowered maybe one or two stalks, not hardly setting 2 million seeds, but a few hundred to be sure. Worried about the larger one mostly. Nearly 3ft bredth in one season and many stalks. Feel pretty dumb now that I know what it is.

How is it that you got your hands on loosestrife seeds? I'm curious to hear the whole story!

I didn't. My neighbor had one stragling little stem in her yard. Neither of us knew what it was. (We had this convo just last season). She said it came back for a few years and she never pulled it. Lo and behold, it started growing in my yard last summer. Like I said, I had planted Astilbe and assumed that is what was coming up so I let it grow. My astilbe never came up apparently. So here it's spring and I'm reading up on proper pruning for my plants and I identified the thing. Funny, I mentioned it to the hortoculturist at the nursery and she didn't bat an eye and actually had some for sale! I didn't take a close look so I don't know if it was purple or not, but wither way,.... wth?