You can always salvage a section of the grass & replant. It will soon grow into a sizeable clump.

Yes - we need to know what sort of 'Knotweed'. If it is Fallopia japonica it would be worth sacrificing the Miscanthus a thousand times to get rid of F japonica.

Well that's definitely not F. japonica (phew!), and doesn't look like a Polygonum/Persicaria, which is the other 'knotweed' I know (although I don't know much compared to others here). Can you take a picture of the whole plant?

No, that's not any kind of 'Knotweed'. May be Aegopodium podagraria ie Bishop Weed. But a picture of the whole plant would help.

^Sure looks like goutweed to me, and it's the non-variegated one which is supposed to be even more invasive...good luck with getting rid of it. It seems every bit of root becomes a new plant...it would be really hard to extricate it from within other plants.