I have discovered that adding a low pass filter in between the last op amp stage and the ADC like shown below improves the distortion performance of the scope.

This has -3dB frequency of ~170MHz, so it does not lower the bandwidth of the scope. Rather, as mentioned in the datasheet of the ADC08100, the circuit absorbs energy coming out of the ADC input.

Below are triangle waves measured using scopes without and with this modification.

Without low pass filter:

With low pass filter: