Question on EPS graphic not scaling correctly

I have a logo that was created for a client that isn't scaling correctly. The company they are using to create a vinyl banner for their store is stating that the logo is pixelating pretty bad when they try to print it.

Does anyone know a fix for this or maybe can provide some detail.

The logo was created in Photoshop as a jpeg and then later converted in inkscape to eps file for vectorizing.

Any help would be greatly appreciated.

Thanks