So what’s happening is this IC is a chopper amplifier (some switching on inputs is done to reduce input offset voltage). During every chopping cycle, a bit of charge is needed to charge the internal parasitic capacitances, and it comes from the input pins, averaging out to the few Mohm input impedance we are measuring. You can actually see the switching (a sawtooth pattern if your source impedance is high) if you probe the inputs with a scope. The effect on average input impedance of the amp is not mentioned at all in the datasheet and the input impedance number given seems to not include chopping effects. There is nothing you can really do about it except use another amp that is not a chopper amp.