I think the only way to keep this so that you wouldn't need to edit the colours depending on each client banner is to remove the green and replace it with an'almost' white (i.e not #FFF)
If you are using any particular colour there is always a chance that it will not be complementary to the banner or logo of the client.
Alternatively you could use a lower-opacity version of the most dominant colour in a banner in place of the green. This would be different for each client though.
I would also suggest
Making the Morrisons logo a little smaller in the boxes - (at that large size the colour here is distracting),
Changing the colours of the Push and <3 icons to the neutral tone of almost black (just like you can see on this GD.SE site), that would go with the almost white. Or if keeping the colour, maybe even placing them elsewhere (like the menu on the top right of my suggestion below)
- though of course I am not sure of your app or its function so that is entirely your choice dependent on if it would be a suitable user flow.
I would also suggest allowing the banner to take up the space at the top, though I'll leave this to you, of course. It might look best to perhaps make it larger to fill the space some more and leave the icons down where the back button is.
There is some basic colour theory covered here and in relation to digital displays in particular here
Good luck with your work.