Yes, AutoExit is there but the Delete button is greyed out. Help!
Probably because it is stored in a different template. You'll need to open
up that template to use that Delete button.
To find the template holding it, use the Macros In: menu underneath the
list. By default, it says "all active templates" but you can use it to
switch through all possible templates. AutoExit will only show up in the
list when the template containing it is listed.
Once you figured out which template, search for that file name. Open up the
file in Word. Then go back to Tools>Macro>Macros, select the AutoExit, and
click Edit. This will dump you into the Visual Basic Editor. Scrutinize
the code under the AutoExit macro and see if it is doing anything you want
it to do, before you just delete it. (If this is a work machine, someone
else may think you need that macro--if it's your home machine, it's less
likely you need it). Use Word>Close to return to regular Word.
Alternatively, find the right file, duplicate it and move the copy to the
desktop, then delete the macro. You can always get the AutoExit macro back
from the copy of the file if it turns out it was doing something you needed.