Question
what do I use to kill green fuzzy caterpillar eating off  growth

Answer
Well if it is only one or two (and they are big enough to see), I would pick them up (maybe with tweezers or something, to be safe),and throw them out or step on them.

If you are confortable using chemical pesticides, you can try Sevin 5% dust from your local Ace Hardware store.  As with all pesticides, you will have to use caution snd follow the label carefully.

Your local garden centers should also carry several natural and botanical products.  Generally, these are safer to use but are probably less effective than  the chemical pesticides. You can even try a mixture of dish detergent and water and spray directly on the caterpillar.

Keep in mind that caterpillars are voracious feeders but they do not lay eggs in their juvenile stage so eventually they will disappear on their own.

DC