1st, go to Tools > Auto Import Options, and turn off "Run Auto Import in the background"
Now, make sure you're external drive is connected, then, from within MC, select all the TV shows you moved from E:\TV (MC should be displaying the missing file icon for these files indicating that they are not where MC expects them to be), right click the selected files, choose: "Library Tools > Find and Replace"
Click on the "Select none" button, then find "Filename" in the list on the left and select it.
Put E:\ in the "Find" field
Put G:\ in the "Replace" field
Hit the OK button.
This will reconnect all the files, preserving any associated library data.
Go back into the Auto Import options, turn the background option back on, and while there, ensure that "Fix broken links" is set to protect network files. This will prevent auto import from removing the TV recordings from your library if you ever run MC without the external drive connected.
-marko.