Removing artifacts from Client's compressed jpeg copy of vector art unsuccesful

New client's only graphic asset, currently being used for signage, business cards and flyers. Unfortunately, they don't have the vector original. So I am working around this compressed jpeg which they cut out some of the silhouette along with the text. I tried using Photoshop (filter>noise) to remove artifacts but it just doesn't help sharpen a jpeg copy of vector art.

Learn Photoshop - How to Remove JPEG Artifacts