Generally, the inputs will have some resistance feeding them, so the resistor shown has the effect of simply reducing the input voltage seen by the amp.
This has the effect of slowing the amp's output response, such as for an open-loop comparator (perhaps presumably, as shown?), or reduces the loop gain when closed.
The term usually used to measure this is noise gain, because the amp's input-referred noise is multiplied by the feedback ratio. When the feedback ratio is lowered (by loading the inputs with extra resistance like this), essentially the amp is less able to control its output, and thus its internal noise makes up a larger fraction of the output.
This is almost always undesirable, so resistors are not often placed in this location.
Two typical examples where it is desirable:
- Note that, by employing voltage dividers at the input(s) -- including between the inputs themselves, potentially -- the common mode input voltage VICM can be reduced. By nature of the divider(s), differential voltage is reduced as well, hence the increase in noise gain. Consider the case of a current-sense amp, using a 5V rail-to-rail type op-amp, sensing a 12V supply: we employ a differential amplifier configuration, but VICM will be nearly 12V if we use the diff amp circuit verbatim, greatly exceeding the 5V range of the amp. If instead, we bias the inputs down towards GND, we unfortunately lose some of the input signal we're sensing, but we can bring the inputs within limits, making the circuit function at all. Thus, it can be a functional requirement, while the increased output noise is a tradeoff.
- Using a decompensated type amplifier. Unity-gain stable op-amps are abundant, so we don't encounter these too often, but they are handy from time to time. These are amps with excessive gain, so that they will oscillate if wired as a voltage follower, or anything with similarly low noise gain (and thus, usually, overall gain as well). Such amps are primarily chosen when at least a modest overall gain is required, for example whereas the TL081 is good for 5MHz GBW, meaning about 5MHz bandwidth at gain = 1, 500kHz at gain = 10, etc.; a decompensated version might have 50MHz GBW but the same phase shift, so it's wildly unstable at gain = 1, but offers 5MHz BW at gain = 1, a considerable improvement -- for no additional supply current. Anyway, all that said -- suppose we need to use one at lower gain anyway; perhaps we only had a dual or quad device handy, or don't want to add another op-amp to the design and would prefer to keep reusing the one type (BOM item reduction). If we need to use one at a gain of say 3 to 5, we can put it in a circuit with a noise gain of 3 to 2 times higher noise gain, and it will remain stable -- as long as, again, we don't mind the increased noise.