Any debris it can dislodge from the moon will be substantially smaller.
And even if it was bigger, and it dislodged bigger rocks, these rocks would basically stay in the same orbit around the Earth as the moon is. The extreme amount of dV it would take to escape the moon’s existing orbit in the right direction so as to fall anywhere near the Earth makes this scenario improbable. I believe (don’t quote me) that we are talking on the order of 10km/s.
Is this true though? It could dislodge larger rocks with smaller velocity, right?
... And wrecking our satellites?
How many satellites have to be destroyed to create chain reaction of debris destroying other satellites/polluting orbit with enough debris so its permanent danger zone for satellites and rockets passing through?
It is unlikely that the amount of debris would reach Kessler Syndrome-levels of orbital pollution, which is what you are describing.