Website redesign issue

Hi all, I'm looking for a little advice. I have been a freelance graphic designer and just finished school for web design. I am looking to add more experience and websites to my portfolio before really seeking out work.

I came across a local company's website (whom I frequent) and saw their current design was poor. I designed a mockup of a page I had in mind for a redesign. I approached them with an offer to redesign and maintain the updates for the site, all at no charge (trying to help the company while gaining experience for my freelance business).

I had assumed they maintained the site themselves. After they agreed and were eager to use my design. But afterward, I heard from the current web "designer" that they wanted my files after I designed the pages and they would be taking care of the updates and upload.

Had I known another designer was in the picture, I wouldn't have made my offer. Seeing I offered a redesign of a website, you can only imagine how poorly done the website was in the first place.

My issue is, the person who had created the initial site and will do the updates, I see has no design skill nor much html knowledge. I am seeking to build a name, a reputation for myself. Once I let go of my design files, I'm out. This person could literally destroy the site I worked on with their lack of design skills. They also have the site featured on their portfolio, would they still try to claim credit, even though it is my design and code?

Seeing I'm new at all this, I'm really not sure what to do. Do I talk to the company in question with my concerns? Do I walk away to not risk ruining a good reputation I'm trying to gain? I want to help the company have a nicely designed website, but yet I want to help myself gain clientele.

I would appreciate any input on what to do from those with experience.