2 options:
1. Suck up the loss, don’t deliver their code.
2. Sue them in small claims court (if your state allows you to sue someone from out of state, California does) as the CI license obviously does not hinder their ability to use the app you created in any shape or form (they are literally allowed to do anything with it).
Your contract should have a line that says all legal disputes will be handled in the [Name Your County], [Name Your State]. Your contract should also mention that you may use open-source software and third party libraries as long as the license of those libraries does not interfere with the clients “right to ownership” of the delivered goods.
I’ve went through this twice in the past, and won my case both times. In Santa Barbara county it costs no more than $75 to file a claim, usually $50 for the range of damages I am seeking (this is also why you should have a payment release schedule, so the amount of work the client has not paid you for yet never exceeds $2-3K).
Don’t forget to document your time working on your case as well - that’s lost wages and you can throw that right on top of how much you are suing for.
Finally - why didn’t you tell them you were using CodeIgniter from the beginning? It’s always much, much, easier to be honest and open from the get-go.