How do gravitons make time go slower?

I hope that you are aware of the fact that gravity can bend space time. If the gravity of a planet (p1) is huge compared to another planet (p2) the time on p1 will be SLOWER compared to the time on p2, this is because the larger the curvature caused by gravity, the larger the time difference. However the gravitons are a medium through which gravity can travel and can't make time go slower unless they are present in huge concentrations.

I believe a possible answer to this problem relies on understanding the ingredients involved and the scales involved. Let us speak first about the ingredients and the definitions.

We can speak about time dilation only when we have at least two frames of reference, $A. B$. That way we can say "time flows slower for reference system $B$ w.r.t. $A$". How do we do it mathematically? We compare time intervals among the two systems to find $Delta t_A$ and $Delta t_B$ are either equal or not.

How does gravity come in? Well we know general relativity (GR) tell us how the metric, $g$ evolves given a energy-momentum tensor (a energy, mass distribution). The metric is the object that describes the time intervals. So, so far no quantum field theory. This is indeed enough to describe gravitational time dilation because it is a phenomena that pertains large masses and large length scales, since we are speaking about distances of order speed of light (allow me the theoretical units speech).

Since GR (which describes gravity) is the one responsible for this time interval differences, we say that gravity causes time dilation.

Now you must understand that the graviton is the name give to a quanta of the gravitational field and at larger scales, the field description is more appropriate and allows us to compute things.

Mixing both worlds, we arrive for example at quantum field theory in curved spacetimes, where one usually uses an Ansatz for the metric, which will be a background (sometimes dynamical, sometimes fixed) to explore its impact on particle physics phenomena, such as scattering processes. Therefore in this cases since we are interested in smaller length scales it is more useful to speak about single particles instead of fields (at least before you actually have to compute the amplitudes associated to Feynman diagrams). Here the graviton appears again (understood always as some asymptotic state), however most computations occur within a fixed reference frame given by the background chosen. So time dilation effects are not important. At the end of the day it is like trying to describe how the discrete levels of the harmonic oscillator are related to a basketball bouncing. My final message is then "Physics at greatly different (energy) scales decouple".

I hope the discussion above clarifies some of your questions.