Q.Can A Pussy Willow Bush Be Revived After Aphid Infestation? Some Green Pliable Branches With Leaves
In the 5 years in this house we have never had this happen to the bush. No live aphids seen on the bush but I did cut down new growth from base of bush that were covered in them.

Certified GKH Gardening Expert
I'm surprised the whole bush didn't have them. I suggest treating the whole bush for aphids. You an buy a commercial remedy or make your own. Here is more:
https://www.gardeningknowhow.com/ornamental/shrubs/pussy-willow/growing-pussy-willows.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/homemade-aphid-control.htm