How do I filter the water from my home gutter system?

Because of the terrain, my gutter in front of my garage is below street level. For this reason, connecting to the public rainwater network is out of the question, because In the event of a heavy rainfall, the water from the public network would gush out of my gutter. As an alternative, I would direct the water to a cistern and use it to water the garden. The plan is for the overflow to seep into the property.

Now I have a question: since my car, etc. is parked in the yard and all the tires and brakes wear out here, these "toxins" will get into the cistern..... Is there any way to filter out this fine dust/abrasive, etc. so it doesn't get into my garden?