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I don't know anything about Inkscape, sorry. You might try this as a workaround. It may not work on all images if they are intricate or have a lot of curves. Ctl/cmd click on the thumbnail of the image layer to make a selection. Go to select>modify>contract and enter one pixel. Either invert the selection and dlete the pixels or mask the image. I would always mask if I want to check edges before committing to the deletion.

You still haven't said what resolution you are working with. That could be making a big difference. The higher the resolution, the less problem you should have.