I most cities, you can recycle (reciclar) some of your trash. Sometimes, you can even be given money for it.
When I was a kid in Madrid, there were some places where you could bring used paper (to be recycled) and you would get some money (very little per Kg. of paper or cardboard). We would say that they bought the paper from you. This was way before we started to have different trash containers for garbage in order to separate and recycle.
In the United States, you can not only recycle soda cans and other bottles (glass or plastic) but you can redeem (redimir?) them.
That picture is from a bottle of coke, and basically says that you can get 5 cents back for the plastic bottle in the states of Maine, Vermont, Connecticut, Massachusetts, New York, Hawaii and Iowa, and 10 cents in Oregon and Michigan (and I don't know what the heck they do in California...). It's similar for cans and some glass bottles.
To get that money you may need to take the bottle to a redemption center (centro de redención?), a liquor store or some other designated places.
Many people take advantage of being able to redeem paper, plastic, glass or cans for money. From people who have little to subsist (and benefit from collecting and redeeming what is garbage for other people) to others which may collect, redeem and then donate the proceedings as they see fit.
I understand that most cities have programs to recycle garbage, but I don't know what they do in order to redeem recyclable garbage for money (that is specific of each country, city or state, as seen in the coke label above) or what do they call this action.
As I said at the beginning of the question, a lifetime ago I would had said in Spanish that someone would "buy used paper" from you. I understand that not all Spanish speaking towns or cities may offer a redemption program from recyclable garbage. The direct translation, redimir, doesn't seem to be the best in this context.
So, what do you call in Spanish the act of redeeming recyclable garbage to get money for it?