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

Create Custom Banner for Web Template

 This is the first header I designed in Inkscape to replace the generic template header for the CBC website.

Now that I have a created a neat little vector image of the steeple I designed a unique new banner that includes the church motto.

Create Vector Image of Steeple from an Old Church Program

With the limited resource of the poor quality print of the church, I was able to conceive of creating a logo/avatar based on the churches own steeple. Simply created a simple vector drawing in Inkscape by tracing a cut from the original image.