Yes—rather than blurring freehand, make a narrow selection that follows the edge, then feather and blur only that strip.

A practical GIMP workflow is:

1. Select the background near the hard edge.
2. Grow the selection slightly so it reaches the edge.
3. Use Select > Border to create a thin band that straddles the subject/background boundary.
4. Limit that band to only the areas that should be softened.
5. Feather the selection by a few pixels, roughly matching the blur width you want.
6. Apply Gaussian Blur.

If you already have paths, they can help define that edge region accurately.

The key idea is that a feathered edge selection lets some subject color bleed naturally into the background, which looks much more realistic than simply running the Blur tool along the background side.

If you use a tablet, painting the Blur tool with a soft brush along the edge can also work well. With a mouse, the feathered border + Gaussian blur method is usually easier and more consistent.