It is moral to clean up after yourself. Cleaning up after others is a job that demands payment. Cities must tax advertisers so they can employ people to clean up after them.
Throw the card in the trash, like a decent human being.
They are counting on people being decent human beings who do what they're supposed to do without complaint. That's exactly what enables them and lets them get away with their unacceptable behavior. If nobody did that, maybe the situation would become unmanageable and the city would be forced to deal with it.
The right thing to do is to put an end to all advertising. That's the true solution. Nobody's gonna do it because the money speaks much louder than right and wrong.
Decreasing effectiveness is kinda hard, so for short term putting on a trash can I guess, for the long run littering the street can be better option (can maybe push city to increase fines etc for this kind of advertisement)
I was thinking more as tool for insurance and/or attempting to force the company to pay for the cost of an exterior detailing of your car since they plastered something to it (with the help of the weather).
In many US areas there are online police reports for minor incidents and the purpose of the report is almost solely so that you have a record for insurance.
It may also help if you call up the company (or publicly shame them with a tweet) to ask for reimbursement for the cost of a car detailer to remove their litter from your car without damage. Having a police report means you could put it all in the hands of your insurance company who have lawyers on staff or use it as part of the negotiation with the company.
Maybe enough police reports about a given company and you could petition the council to revoke that company's ability to flyer any longer?
I know I'm probably dreaming that it would make a difference. The only time I've had an experience with this a friend used twitter and got a public apology from the company along with some monetary compensation around the removal of the ink residue from the windshield.
People that put the flyers on the windshields are just a step from insolvency, so no use to go against them. The "company" behind them, just a little step up the food chain.