hi FBS,
Any differential voltage at the OPA, due to manufacturing variables will be integrated.
Depending upon the sense of the offset voltages the output 'swing' will be offset from zero.
You could try injecting a low level voltage into one of the OPA inputs in an attempt to cancel out the offset but the long term and temperature stability will be unpredictable.
EDIT:
This is what I see using LTSpice
I used Start DC supply at 0V.
Also note that for a -200mV down step followed by a +200mV up step [of same duration], the Vout ramp will not swing thru 0V.
All you have done is charged the Icap by a fixed amount and then discharged by the same amount, so thats 0V upto +Vmax out then back down to 0V.
Added a 2nd image, the +200mV duration is now twice that of the -200mV step