Looks like an integrator Given the input impedance of that op amp is around 10^13 ohms, 100M isn't a lot. Sure you need good construction technique (and actually need this circuit) but there's not that much weird with it.
(There are similar circuits with much higher resistances)
A physically larger resistor will be less subject to leakage (after cleaning).
However you also need to be careful in the selection of C5 as you want something with low leakage and also keep that clean. typically polystyrene capacitors are used in these circuits but due to the relatively low 100M resistor of recommend something else (some other film capacitor should be fine) mostly because polystyrene caps can't be cleaned with alcohol, and that's probably the best solvent to get rid of finger grease.
Whilst it's not absolutely essential, if you lift the pin for the inverting input so it's sticking in the air and connect the various other components to it directly, you will eliminate many of your other leakage issues as long as you keep the IC itself clean.