Huh?
What purpose could that serve as a "local ordinance"?
It is probably to allow time to see if the gun is reported stolen or otherwise “dirty”. A pawn/gun dealer reports the S/N of the traded-in gun to the cops, and if no one raises any objections within 20 days, it’s probably legit to sell.
The 20 day thing has to do with FFL's being required to report the transfer to them and allow the local constabulary to run a check and see if it was used in a crime.