Do I have to ground my laptop to use the Voltcraft DSO-2020USB Oscilloscope?
When you measure a voltage on an oscilloscope you apply the voltage between input and the ground of the oscilloscope. There is no other way to do this unless you would use an isolated probe.

The ground of an oscilloscope should be connected to mains earth so that it has a ground connection. The oscilloscope can work without the mains earth connection but that is not recommended for safety reasons.

When you measure any device with a grounded oscilloscope then the device will be grounded when you connect it to the scope as the oscilloscope is grounded and you connect the device to it making it grounded as well.

Devices like laptops are either connected to ground already, the only way to be sure that this is the case is to disconnect the power adapter from mains, connect it to the laptop and measure the resistance between the power adapter's mains earth connection. That is if it has such a connection, if it does not the laptop is not grounded (through the adapter) but floating. Sometimes there can then be a small spark as you connect the scope's ground to the laptop. This spark is harmless assuming the laptop's power adapter is designed properly.

If there is a low resistance connection then the laptop will be grounded if you use a mains socket with a ground connection.