I have a handful of cloths that I've used to clean and grease my bike chain over the years. Each is covered in chain grease and other gunk that was once on my chain. I'm starting to wonder what I should do when my latest cloth reaches peak grossness.

It seems like there are two obvious choices:

* throw them away and acquire new ones  

I'm not sentimental about these cloths, but I would prefer to not create unnecessary waste. I'm also vaguely aware that municipal waste forbids certain kinds of things, and maybe chain grease is one of those?
* wash and re-use them  

Sounds okay, but what kind of soap would I use for this? And what happens to my city's water system if everyone does this (to say nothing of the plumbing in my home)?

Casual googling seems to turn up a lot of this: "soak all your rags in an ambiguous cocktail of noxious cleaners, then throw them in the washer and dryer," which sounds to me like a good way to accidentally create mustard gas, ruin my clothing and appliances, and court a house fire. And it ignores the question of what happens after that cauldron gets emptied into my kitchen sink or bathtub.

How is a reasonably conscientious person supposed to deal with their chain-cleaning rags?