Here's a trick that will work well.
Make a Color Matte that is the same colour as your darkest area of background. Place it on a layer below your footage. Set the Blend Mode of the footage to Darken. All the nastiness will magically disappear.
If the result looks to dark to you, apply an Adjustment layer above those two layers, go to the Lumetri panel and adjust the levels to taste.
(Because your display is badly adjusted, you will also need to add a temporary adjustment layer [before doing the final colour adjustment) and add a Gamma correction to bring the brightness way, way down so you can check that you have fully eradicated the problem.)
Simon Ubsdell
hawaiki