I have never figured out if this can be done.  When I mark out an area with the bezier, instead of obtaining the area I marked within the bezier, I want to extract everything except the cut out area.  Is there any way to do that?  Thanks

In the Object tab you have the option to use set clip or set inverse clip.

When I do the inverse, I get the same results as using Set.

With objects it works well. With images, try this video, I think it's a good solution. https://www.youtube.com/watch?v=tIOEKX11JCo

I see how that works with objects, but I don't think that it will work with bezier cutouts.  I am going to try bezier cut a portion out of an image, take it to Gimp and try to change all colors to white.  Then paste it back into Inkscape over the area I want and do a trace bitmap.

UM22.04 Inkscape 1.2

Watching video from @mrks9 I drew a shape and put in rectangle selected both and duplicated. Followed video with one, dragged (path difference) over image and then raised above image and set clip. Then with other set (rectangle and shape)dragged over image and selected just the shape and image and set clip. Rectangle was just used for alignment. Don't know if this is what you are looking for.

Inverse clip works with image turned into pattern.

Perfect!

1. Paste image into Inkscape.

2. Focus image and do an Object/Pattern/Objects to Pattern.

3. Draw around area to remove with bezier.

4. Drag cursor around image to focus both image (now a pattern) and bezier line.

5. Do an Object/Set/Inverse.

Thanks to all.