simple enough. It's illegal.SEC. 28.01. HANDBILLS – DISTRIBUTION.
(Amended by Ord. 168,321, Eff. 12/13/92.)
(a) No person shall distribute or cause or direct the distribution of any handbill to passengers on any streetcar or throw, place or attach any handbill to or upon any vehicle.
given the fact the OP's organization does not have the right to tow vehicles in a public roadway, I suspect the argument about informing the car owners is an intent to hide the use of the distribution of hand bills to advertise their event.
as I said; since the city would be responsible for towing illegally parked vehicles and the city is the only entity that can actually declare it would be illegal to park on the street, the obligation is on the city to provide legally adequate notice to people parked on the street and putting flyers on cars ahead of the event does little to provide actual notice. Signs that are still there once the flyer on the car drives away are most likely required to be posted.

SEC. 28.01. HANDBILLS – DISTRIBUTION.