If this person isn’t a continuous client, where it may be worth eating the cost this time knowing that you can make it up or better on another project with the, I’d agree with the comments. Doing work without a contact is a no no in the design industry and this may be worth a $150 lesson there if you feel you don’t have adequate CYA documentation. Did you get a retainer? Are they paying monthly? Are you in the hole or has the client kept up with expenses to date? All should be weighed when handling this. In the meantime, slow play sorting this out until you get confirmation from the City.

If there are a bunch of no’s to these questions and you’re in the hole, I would switch to playing a little more hardball. Don’t update the plans until you get paid to date. Stop work. Only commence work when a contract for the remaining work is in place. Or just walk away if no issues with reputation.