What component of the oscilloscope controls the electron beams to display data on the screen?

The component of the oscilloscope that controls the electron beams to display data on the screen is the CRT, or cathode ray tube. The CRT is a crucial part of traditional oscilloscopes that generates visual output by directing electron beams onto a phosphorescent screen. When an electron beam hits the screen, it causes the phosphor to glow, creating visible traces that represent electrical signals.

In context with other options, the digital display refers to more modern oscilloscopes that use LCD or LED screens to present data but do not involve electron beams. The power supply provides the necessary energy to operate the myriad components of the oscilloscope, and while it's essential for functionality, it does not directly control how data is displayed. The probe is a tool used to connect the oscilloscope to the circuit being tested, but it is not responsible for the display mechanism itself. Hence, the CRT's role is fundamental in controlling the visualization of electrical signals, making it the correct answer.