You cannot remove a Restrictions passcode be restoring a backup. Either use a backup before you set the passcode or:
Placing your device into recovery (DFU) mode:
Follow these steps to place your iOS device into recovery mode. If your iOS device is already in recovery mode, you can proceed immediately to step 6.
1. Disconnect the USB cable from the iPhone, iPad, or iPod touch, but leave the
other end of the cable connected to your computer's USB port.
2. Turn off the device: Press and hold the Sleep/Wake button for a few seconds
until the red slider appears, then slide the slider. Wait for the device to turn off.
* If you cannot turn off the device using the slider, press and hold the
Sleep/Wake and Home buttons at the same time. When the device turns off,
release the Sleep/Wake and Home buttons.
3. While pressing and holding the Home button, reconnect the USB cable to the
device. The device should turn on. Note: If you see the screen pictured below,
let the device charge for at least ten minutes to ensure that the battery has some
charge, and then start with step 2 again.
4. Continue holding the Home button until you see the "Connect to iTunes" screen.
When this screen appears you can release the Home button:
5. If necessary, open iTunes. You should see the following "recovery mode" alert:
6. Use iTunes to restore the device.
If you don't see the "Connect to iTunes" screen, try these steps again. If you see the "Connect to iTunes" screen but the device does not appear in iTunes, see this article and its related links.
Note: When using recovery mode, you can only restore the device. All user content on the device will be erased, but if you had previously synced with iTunes on this computer, you can restore from a previous backup. See this article for more information.