50 ohm terminator -- voltage divider?
The signal generator we use in our university behaves in a similar manner: if you load it with \$50\Omega\$ the output waveform amplitude is exactly what you dial in the SG. That's because our signal generator has a settable load impedance: you can set it to \$50\Omega\$ or to \$\text{HI}_\text{Z}\$, the latter meaning "high impedance".

What does the SF actually do? When you set the load to be \$50\Omega\$ it doubles the output amplitude so that on your line you have what you set, but if you set the load to \$\text{HI}_\text{Z}\$ the output amplitude is what you dial in.

You can see if that's your case removing the termination: since the scope input impedance is very high, and negligible as you suggest, you should see a doubled wave. If you can dig up the setting you can try to set it to \$\text{HI}_\text{Z}\$ and then connect the cable with the termination: you should see a wave that is only half in amplitude.

If you are not sure that this doubling/halving is done SG side but you're afraid it's something scope side, that is very, very unlikely, take your multimeter and measure the output rms voltage.