I don't know about nixing it, but it looks "cut out" in places.
Here's what I do to clean up a BG a bit when there are shadows or wrinkles. Select the BG using either Select -> Color range or the magic wand. Switch to quick mask and clean up as needed. Then feather the selection by 5 px. Load the selection as mask, reselect the image and reselect the selection - copy to new layer. Gaussian blur at something pretty high like 45. Then move the mask up to the blurred layer.
Sounds long and complex but it's really only a minute or so including making the selection.
...btw...the parts of the drop that have been left (for example around the paw on the first shot and in between the dogs on some of the others) was done intentionally. I thought the image looked odd without the texture - particularly on the first shot.
Should I nix it?