Note that it is not enough to measure the amplitude of the frequency response, in order to preserve the pulse shape, one needs phase also. That can be somewhat difficult. Only knowledge of complex frequency response (magnitude + phase) enables the calculation of proper compensating filter. Of course, this can't be stretched very far, and all factors to be compensated should be stable, otherwise the compensation will make things worse. And like said, the noise will increase.
But, this can be done offline without any changes to the scope in case somebody wants to try it out.
Regards,
Janne