The Local Fresh Wholesome shop for Neugarten has a range of cordials which act as filters. They will tone down the backdrops or even give them a subtle new hue. Play around with them in the Wardrobe - Uncheck the Only Show Items You Own box and then search for them by name. You don't have to own clothing items to try things on.
They cost 85,000 sP and Neugarten ends 11:59pm on July 5th. The most useful one for you right now might be the White Grape Cordial.
You can also use the coloured cordials as backgrounds in their own right even though they are labelled Foreground. Just move them down so they are beneath the base.
The cordials are nice, but:
I've actually just used a cordial to darken a background a bit, and it works to slightly dim a background, but not at all for what I want gradient backgrounds.
Rather than try to explain, I threw a gradient in photoshop:
Black strong gradient (top)

Blue strong gradient (bottom)

Together over a background:
(Background: )
Purple soft gradient (bottom)

Used over a background:
(Background: )
Snagged those two outfits from the Stimulate your Style raffle because I didn't want to spend hours making some just to demonstrate.
They also work pretty well as a background on their own:
Baby blue soft gradient (bottom; top)

Pink strong gradient (bottom)

As a background in their own right:

I see what you mean now. Two items which have this kind of effect are -
It would be useful to have other colours.
Ahh, at least they're available in black! But other colours, and varied opacities, would be great.
Full support for more BG items! There are tons of great real world suggestions in the first post that I would love to see. I think it would be neat if we could get some BGs directly based off of the different areas of subeta, so our HA could "visit."
I also love 's idea of more plain color BGs and gradients that would be easier to layer. Using those body lotions they mentioned is particularly a nuisance, because most BGs have too much going on and end up looking off when a sky item is layered on top.
I added all the background suggestions. While I'm not opposed to asking for layerable pieces to be included in the new backgrounds search, there's a suggestion thread already here asking that the chair items become wearables - so it might be best to toss in the suggestion for the Home Goods furniture there. And there is a suggestion already from for a background with fancy wallpaper and a fainting chair together (trying not to duplicate requests if I can).
Got your suggestions both up in the top now too.
Antimoany, there's a link to your more detailed explanation post too (thank you for that!)
I'll add it to the top because it's meant to be a background item I think.