unable to access my PC

I was recently using a hotel PC to acess my PC. I logged in to Team Viewer, selected the PC I wanted to access from the list and then a window popped up saying I had to access my email to verify the device I was logging from. The problem was that until I could access the PC I couldn't read my e-mails. How do I overcome this problem in the future especially as I am planning overseas travel soon?

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