Sounds like you're talking about a Logon Script specified in a GPO, rather than the GPO itself.
You can prevent the user from closing the script by disabling the policy to run logon scripts visible. Have a look in Group Policy under User Configuration / Administrative Templates / System / Scripts at the "Run logon scripts visible" policy.
By default logon scripts don't run visible so you must have a GPO somewhere that's setting this to be visible. I'd be sure that you know why that was done before you go changing it now.
Edit: As @Shane Madden mentions, it's possible that the window the user is closing could be a "Legacy Logon Script" (specified on the "Profile" tab of the user account's properties in "Active Directory Users and Computers"). If that's the case, have a look at the "Run legacy logon scripts hidden" policy located in the same place mentioned above.