Well, first this is PaintShop Pro. A different beast from Photo-Paint. So I don't know how useful my suggestions would be. This might be better suited in the CorelDraw community.
http://coreldraw.com/
But what I would do is create a selection around the petals. In this case I would use vector paths to outline them but everyone has their preferred method for creating selections.
Then invert the selection to select the background. You can then delete the background and start over, probably with a simple gradient, or you can smooth out the image. and hopefully get rid of the artifacts.
If Photo-paint has one you could try to remove JPG artifacts using a filter of some sort. PSP has a "JPG Artifacts Removal" filter found under the Add/Remove Noise section of the Adjust menu. No idea where it would be on Photo-paint, if it has one.