I don't understand where you click connect and where you want to change the login settings? Is it that you get logged in to the remote system or is it the TeamViewer account? On the website or in the app? For the website, delete the login credentials in your browser, in the app, logout from your account and before you login again uncheck „keep me signed in“. If it is the remote system, i don't know how you do it, give me a hint. In general i don't see where it is unsafe, as long it is your computer and you are using strong enough credentials there. If you grant access to your computer account to someone else this is the point that is not secure and then it doesn't matter if or if not you save your credentials.
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