I've used the same Park Chain Cleaner tool for years. After each use I just spray some whatever degreaser I'm using (now working my way through a jug of Simple Green, have used GreenShield in the past) on it and let it soak while I lube up the chain and any other bike maintenance I"m doing. When I'm done and putting everything away, I dump the degreaser out on my lawn (no grass has ever been harmed with this process, not even the weeds...) and spray into the chain cleaner with my hose, spinning the brushes, etc.
About once per year, I'll take the brushes out (as someone else pointed out, they come out pretty easily) and spray them with the degreaser and let it soak, then wash them off.
Over the winter, when my hoses are off and I'm doing this indoors after using the tool to clean the chain, I fill it with warm water and run the chain through it again, to remove the degreaser from the chain before applying lube to the chain. That keeps the cleaner clean enough over the winter.
On the environmental note, the science is on the side of sal's post - I liked using GreenShield to feel better, but ran out and had the jug of SimpleGreen around. But, a lifetime of chain cleaning doesn't come close to one day of washer and dishwasher draining into my septic system.