I seeded it on December 21st with a short grass prairie mix heavy on butterfly flowers, it has prairie drop seed, side oats grama, little blue stem, it also has hyssop, coreopsis, coneflowers, butterfly weed, asters, liatris, prairie clovers, the usual prairie flowers... Right after I spread the seed, I covered the area with a thick straw mulch...

So now this spring, the area has some type of speedwell (veronica/figwort species) growing actively right through the straw, all over. (I am figuring that the straw had the seeds in it?) I'm thinking to myself (and I know that i would tell other people) that the speedwell is not going to outcompete the natives once they get started. But I really don't want the stuff spreading into the lawn areas or my neighbors lawn.... so I am considering hand picking it out... except isn't speedwell, one of those rhizomatous plants that will spread even more if hand weed it? Maybe I should just get out the round-up again - not my preferred alternative. Or maybe I should just not worry about the speedwell?

But even if you are correct, if I were you I'd jerk it out of there now anyway. If it is new plants from seed, then the chances are good you'll get the entire thing or darn near - if your soil is fairly loose. At the very least, you'll discourage it and prevent its going to seed. And as you say, in a few years the natives will outcompete it, so as long as you keep it at bay until they are ready to do that, it should work. I am just paranoid about using herbicides anywhere near my good stuff. Don't like using them anywhere.