I’m pretty sure it’s the FCA not ASA that are in charge of advertisements for Financial Services.
As much as I believe they should come down hard on Curve, I don’t see it happening without a lot of attention being drawn to it.
If you get hit by free and Curve advertise you as having saved though you could definitely take it to the Financial Ombudsman Service assuming Curve refuse to uphold your complaint (I would actually encourage you to do so) as the more FOS complaints exist the more the FCA will have to pay attention (every FOS complaint is forwarded to FCA)
As for what your resolution would be, I would recommend you demanding changes to the advertising within the app to make things more transparent although this is obviously your choice
I personally will be raising multiple complaints shortly despite being a somewhat satisfied customer with the actual core product.