Testing a batch string for surrounding quotes is quite annoying. Here is a solution for Windows 2000 and newer:

:: %T% contains the test-string
IF "%T:~0,1%%T:~0,1%" == """" IF "%T:~-1%%T:~-1%" == """" (
  SET T=%T:~1,-1%
)

You can see, I am using the first respectively the last character twice, because a single double quote would break the IF. I'll explain it with this little example:
T keeps the string "Hello World!" with the surrounding quotes. The (simplified) test

would expand to
which will be parsed as
with the string being " == " (...). Cannot work, huh?