It looks like a pretty simple logo to re-create by hand, if the customer provided image is sufficiently high in resolution. Nevertheless, our shop does not do free re-creations of such artwork. We tell them up front if they cannot provide a vector-based version of their logo then we'll charge $50 per hour to vectorize it, with $50 being the minimum charge. What's really funny: a bunch of customers will magically find a proper vector version of that logo when warned of the looming art charge. Or they'll put us in touch with someone who can provide that artwork.
Basically the thing that happens so much of the time is customers will lazily grab the very first file they find of their "logo" and email us a copy of that. 9 times out of 10 it's going to be some dopey, low-res pixel-based image. Maybe it's a JPEG image a "graphic designer" gave them to be able to stick in MS Word documents. Or it might be a PNG image they right-clicked and saved off their freaking web page. The customers don't know about differences in graphics file formats or even the difference between pixel-based and vector-based artwork. They just think all graphics files are the same. So any stupid JPEG image should work, no matter how tiny. Just use that "enhance" filter the TV people use on CSI: Miami.
