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As our case also involved neighbours, we had two companies out to quote and both said it was easily managed, mortgage lenders seemed to historically use it as a spurious reason not to lend. The instances of it actually causing damage are very few and massively far between. A rose bush planted next to a house has more ability to cause damage than JPW.
You are right, they are being less hysterical. The plan and guarantee are just like a final stamp to keep everyone happy.
That certainly looks like mid treatment knotweed. Also, slugs do have a go at the leaves.
The treatment takes up to three years before it is declared dormant. Each year it comes back it looks in worse and worse shape. A decent management plan will treat twice a year for 3 years and then check on it for two further years.
Also check that there is a 10 year insurance backed guarantee in case the company treating it goes tits up. That is the more expensive thing so the vendors could have cheaped out and just got the 5 year treatment plan.
DO NOT PULL IT UP OR CUT IT DOWN IF THERE IS A MANAGEMENT PLAN IN PLACE!!!!!!! They need the live plant to be able to treat it. If you destroy the plant you could void the plan and any guarantee. Otherwise, so long as the management plan and the guarantee is there you'll be totally fine.
Again, guess who just forked out for all of the above.