Since the latest macOS update the TeamViewer application is not working or rather the screen is gray. With the following steps you can use TeamViewer also on macOS Catalina 10.15:

Start the TeamViewer (Downloaded from the Dinotronic website)

The TeamViewer is showing the following screen on the customers computer:

Click on "Bedienungshilfen" --> "Zugriff anfordern..."

Click on "Systemeinstellungen öffnen" 

Unlock the settings: (If necessary) 

Activate "TeamViewer QuickSupport" and close the "Systemeinstellungen"

Now click in "Festplattenvollzugriff" on "Einstellungen für Festplattenzugriff öffnen"

Unlock the settings: (If necessary) 

Click on + and navigate to the downloaded TeamViewer application (Usually it's located in the download folder)

Now you have to close the TeamViewer application:

Now reopen the application --> Double click on the download TeamViewer application in the Downloads folder:

Now the user has to grant access to "Bildschirmaufnahme". The user has always to activate this setting.

Now click on "Einstellungen für Bildschrimaufnahme öffnen..."

Activate "TeamViewer QuickSupport"

Now you have to close the TeamViewer application:

Now reopen the application --> Double click on the download TeamViewer application in the Downloads folder:

Now the user has to grant access to "Bildschirmaufnahme". The user has always to activate this setting.

Finally you can click on close and start the TeamViewer connection:

If a user starts the TeamViewer a 2nd time, the user always has to allow the screen recording permissions first: