First of all, you need to check whether both partners are logged into their TeamViewer accounts and whether their devices are connected to the Internet.
Sometimes viruses and anti-virus software are the cause of problems. If everything is in order with the connection to the global network, but the program does not work, check both computers with antivirus, delete the found malicious files. Then add TeamViewer to your antivirus program’s exclusion list.
Restart your computer. Reboot will fix minor glitches in the program. If the next time you log in to TeamViewer, and the Authentication Rejected again, then it means the files are badly damaged. There is only one option left: TeamViewer needs to be uninstalled and then installed a new version.