Luckily it's easy to remove seedlings. I've had crop after crop this year after planting 2 last year. I haven't space to allow them to do their own thing but keep an odd one to produce flowers for the bees and for Pimms but aim not to let it shed seeds. I grow them in succession and will let the last one of summer seed itself. Believe me, they can be a pest unless kept under control.
I just bought a large seed packet for the blue borage to scatter in early Spring down at our rural property in Central TX. I think I'll keep it mostly along the chain-link fence to the pasture. I love the blooms and color. I, too, didn't know there was a white one.
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Borago officinalis alba.....Starflower, Bee Bread, White Borage
https://www.google.com/search?q=borago+officinalis+alba&rlz=1C1CHBF_enGB785GB785&source=lnms&tbm=isch&sa=X&ved=0ahUKEwil14HR6OTjAhVRTxUIHb2mDSMQ_AUIESgB&biw=1920&bih=937