Hi Damaso,
I designed a similar circuit for my mBed module which uses 0 to 3V3 input and my converter circuit made it bipolar.
I have attached it for comparison and thoughts on the possible issues.
Although my circuit is inverting it is quite similar (I also used BAT... diodes, but they were not in my CAD package)
The big difference is the bias of 2V5 in your case and 3V3 in mine.
My circuit provides a constant voltage at the In+ of the opamp and more importantly as it is driven from a low impedance opamp before this a low and constant impedance, hence the resistor R20 in my circuit include additional external impedances is fixed. The importance of this is the 3V3 is divided correctly (I'll come back to this point in a minute)
In your circuit the voltage at the input labled Amp out is as the previous poster stated driving 20K to 2V5 so does have to be able to sink 0.125mA which is not much but could be an issue?
The other point is resistor values, when biasing the inputs for bipolar operation make sure you get the correct gain for each input to ensure the 2V5 is being used as expected. Note in my circuit the 'odd' resistance values to give the 3V3/2 offset I needed. This may not be the same for your configuration but just check.
In summary check how you driving R23, if it's in anyway not near zero impedance then put in a buffer.
The effect from placing of the meter in the circuit to me indicates the drive signal is a high(ish) or capacitive and without the meter your current from R23 is charging/discharging this capacitance.