Ok, it looks like you have lawn, with a plastic runner thingey to keep the grass from creeping into some bed.
What did you have in that bed last year? To me it looks like some flower that might have been growing in the bed that seeded itself out. It does not look to me that the weed is going from the lawn into the bed. It looks like some flower that grew there last year and seeded itself into the bed and into the lawn.
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