Take a look at gimp layer modes.  Maybe dodge mode on a new top layer and
use a rectangle gradient to blend the burned edges inward.  Gradient mode
might be fg color to transparent and use white.
how does one use a transparent layer? is it only for drawing things on? I
have some old pictures that have darkened around the edges. How I think I
can fix it is to duplicate the layer then  lighten the exposure value on
the lower image, then paint black and uncover the lighter image over the
section that has darkened. How do I do this with gradients and Darktable?

-- 
:-)~MIKE~(-:

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