I use TeamViewer to connect my iMac to my neighbours Mac Mini. Both machines are running Catalina 10.15.4 and TeamViewer 15.4.4445.
Until I connect both machines work normally. When I connect, the Desktop on my neighbour's machine greys out., i.e. the Desktop picture disappears. When I disconnect leaving TeamViewer running on both machines, the Desktop picture reappears. Screen Recording is checked on both machines.
Thanks for your message!
Would you mind checking your TeamViewer settings whether Remove remote wallpaper is enabled under Preferences --> Settings --> Remote Control --> Under Display --> Remove remote wallpaper.
Please take into consideration before removing the tick box: Is there a colorful picture on the desktop?
Removing this picture might be a great idea as it would "cost" more power/bandwidth for TeamViewer to transfer all the colorful and beautiful pixels from your neighbors' mac to yours. If you want to transfer and see it: No probs and feel free to go ahead and remove the tick box!
But keep in mind: It might result in a bit slower connection.
I hope this helps you.
Thank you Esther for your prompt and successful suggestion. It did not work immediately, I had to restart my TeamViewer to have an effect.
Interestingly, I had not noticed this effect when connecting to a Windows 10 machine.