That reward as you call it, has created a 2nd level economy in Germany.

It is not only homeless, people with very low pensions or not able to get a proper full time job also hunt for them, everywhere.

On the streets, trains, subway, beach, lakes, you name it.

To the point that many people don't throw away bottles anymore, leaving them grouped outside the trash cans, as means to help those people pick them without messing with trash.

There are even trash cans in the Rhein region that have bottle holders around them.

So yeah it helps keep the street clean from bottles, but fighting the causes of this 2nd level economy would probably be a better idea.

What is the correct word for the reward? That's one of this weird case where I know the word in French and German but not English...

Our public waste bins are designed like this in Vancouver. People put bottles/cans with deposits in a circular metal holder below the rim of the trash bin so that the homeless can pick them up easily. There are a LOT of homeless here. I moved back to Canada from Central America and my first impression of being back in the developed world is my god look at all the homelessness.

That happens in San Francisco, too. You'll on occasion even see someone on the local public transit with a big trash bag full of bottles. I guess they're on their way to a redemption center for the deposit.