[Inkscape-user] Repairing a pixellated drop-shadow gradient

I have inherited a vector PDF and an SVG file of a logo made from outlined letters with a gradated drop-shadow (see http://xml.silmaril.ie/downloads/letterlogo.png for enlarged PNG fragment).

When the logo is enlarged (eg for use on a poster), the drop-shadow shows up pixellated. Both files exhibit the identical problem. When edited, the drop-shadow is indeed made up of pixels. I assume in my ignorance that it was passed through some software at some stage in its past which concretized the drop-shadow as graded pixels.

How would I go about removing the drop-shadow entirely, and replacing it with one of identical color and extent, but done in such a way as to withstand enlargement without deterioration?

Peter