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Given the fact the way her dress looks in the shot isn't very flattering my first suggestion irrespective of your background concerns would be crop tighter, above the bustline to eliminate that defect/distraction. Doing that will eliminate the problem of the distracting background. Here's a suggested editing approach...
Your lighting strategy with cross lighting and very little fill is revealing age and character, but that heavy look is one I personally find more in context with a gnarly grump old man than a sweet old grandmother like this so I softened the overall look using the middle slider of levels. But I did this on a duplicate layer in CS5 and used a mask to selectively blended in the lightened areas only in the shadows of face, hand and clothing leaving the background dark as in the original.
Normally I'd soften skin keeping eyes and mouth sharp. Your image as posted is a bit OOF and soft so here I just selectively sharpened the eyes, mouth and the pendant to recreate some specular highlights and sparkle lost due to the soft focus. Eyes without catchlights read as vacant and dull in photos so I also added catchlights to the eyes which are lacking in the original because the face was turned so much away from the "key" light. They are easy to fake naturally if you use a separate layer, a light gray (off white) color with a feathered brush, then adjust opacity visually.
Tightly cropped headshots above the bustline will often look cramped and unbalanced but the overall visual balance can be restored by adding a mat around the image. Here I used a simulated gold rule to match the gold pendant focal point, and a black mat, which perceptually makes all the shadows in the image seem lighter with more detail by comparison with the mat.