Hi,
What you describe is typical amplifier ringing behaviour on output step.
Surely this is caused by the amp's feedback.
A bigger C at the output can improve this, even better a RC.
Now you say GVW of the amp is less than sampling frequency. I wonder ... but maybe this is the case.
In either case:
The ringing should be rather high frequency, thus it should cause ignorable AC error after the digital filter.
But the ringing is triggered synchronously to the sampling frequency, thus there is a chance that it causes DC error after the filter.
DC error can be canceled out by calibration.
Klaus