Hi Jiri,
I think you can try these 2 ways:
Option 1:
– Use Color Range (Selection > Color Range) to make selection of the background
– Delete background
– Run Layer > Matting > Defringe (eliminate white edge)
Done
Option 2:
– Open Channels palette
– Duplicate Red (or any channel has great contrast)
– Image > Apply Image: Blending mode Overlay (Opacity 100%)
– Load selection from duplicated channel
– Add layer mask
– Retouch if needed
Done
Below you can find the result comparing to the original background.

Regards,