If I use the VPN and remote into my work computer, how will the screensaver lock affect my telework?

The screensave lock should not have an effect on your ability to telework unless you take a break longer than 30 minutes. If the screensaver lock starts, simply type in your password (Faculty and staff using Windows machines will need to enter their Patriot Pass password to access their computers again, while Mac users will need to enter their Mac password).