When a client isn't happy, you're behind the ball. We don't know the attitude of the client or how willing or open they are to changes. So, solving problems like this or even making suggested corrections is questionable. So here we go.
As a business owner what I'd want to do is spend the least time and effort possible to make the client happy. That would be to fix the problem on site. One trick is roll out a coat of red latex, NOVA COLOR, on a sheet of white PVC. Rout out the letters with a 45 degree bit leaving a 1/8" shoulder. This will give an automatic white outline. A little outline would need to be figured in to allow for the V Bit. Then the letters can be quickly applied over the existing. Another option is to create a drop shade effect but that would require some brush skill. There's also the option of creating a semi fat outline and drop shade around the letters using DiBond as an overlay. Red lettering would go on that. I can think of several options but who knows without more input.
It's really not a fair question without more details. At least he did include a photo.
The example photo below show a similar problem. Imagine the maroon letters on a gray background. They wouldn't have enough contrast and would lay there un-distinctive. It's the contrast were after.