With a response like this, I would assume she refer to the design of the websites in your portfolio.
In short, she does not feel that the design is professional enough, or reflect what she is looking for.
Keep in mind that a website for someone selling “makeup” would have a very different layout/design, than someone selling a different product. Especially if it is a web store.
There is a difference from “working on a phone/pad”, to actually “work” on a phone/pad.
Having a responsive layout is not enough, you need to address phones/pads specifically, fixing any possible issues, including changing how the navigation works. This is normally done by having additional css files that is only included on phones/pads.
While this might sounds easy enough, it can be a hassle. All depending on the main design. Basically with phones today need to be handled like we handled browsers a decade ago (i.e. different phone models might require different tweaks).
The best advice I can give in regards to this, is to consider how the website will work on the phone as the same time as you consider how it will work on a computer.
Your response is too defensive. It feels more like someone getting caught doing something wrong, than someone wanting to sell a service/product.
Instead if you try to relate to the customer, you will get a better relations and success rate.
As an example, this is something you could have said:
“I understand your concern, having a website that work perfectly on mobile devices is a must today. If you do not have this, you can potentially lose a lot of customers. When I develop a website for a client, I make certain that the design and flow of the content is easily navigated and read from mobile devices as well.”
Then if you have an example of a website where you have good mobile interactivity, you can add:
“Here, let me show you one of the websites I have created, (show on your phone, or give her the address), as you can see the website is easy to use by mobile device and the information is easily available”
In situations like this, where you do not have anything tangible to show that you know could possibly change their mind, is to thank them for their time.
If you keep trying to change her mind, she will get a bad impression of you. While if you do as suggested above, you have the ability to reach out to her again, when you have a website on your portfolio that you believe will match her requirements.