Transient Response of AC Coupled Inverting Amplifier
C18 is a blocking capacitor. The gain in this configuration is
abs(Gain) = 1/(1+1/(ω∙RC)^2)
Quite contrary to your fears, not fast, but slow changing signals, with the characteristic frequencies less than 6.28/((R14+R15)∙C18) ≈ 10 Hz, are filtered out.
The configuration you used is an AC Coupled Inverting Amplifier. For precise DC measurements, use the recommended ADC driver of the TI OPAx376 document, Section 8.1.3 Driving an Analog-to-Digital Converter.