It is up to the GM
That said, Darth Psyeudoynm's answer is excellent and matches how I would rule in this case, so go read it. What follows is just things I would consider when thinking about this scenario, and I would consider quite a lot of things:
What is the trigger for Aura of the Guardian's reaction?
There are at least two very different answers to this and they depend on the ideas of "damage dealt" and "damage taken". We already have a few questions that directly or indirectly ask about this distinction:
From these we can see that people do not agree whether these are different quantities or not; however, we can look to the Sage Advice Compendium (SAC) for some guidance:
Q. When a creature successfully saves against guardian of faith and takes 10 radiant damage, how much damage does that count against the total amount of damage the spell can deal? Is it 20 because that’s how much it dealt or 10 because that’s how much the target took?
A. It dealt 10 damage to the creature, so 10 is subtracted from the total. (guardian of faith)
The guardian of faith spell states:
[...] The guardian vanishes when it has dealt a total of 60 damage [...]
And from the SAC we can at least conclude that "damage dealt" is determined after resistances are applied. Notably, the answers to the above question arguing that damage dealt and damage taken are different quantities all argue that damage dealt would be the value from before resistances; so one of two possibilities remain:
- Damage dealt and damage taken are the same quantity
- Damage dealt is the value after resistances are applied while damage taken is the value before resistances are applied
I have not seen anybody argue for case 2, and I will not be doing so myself, but it is an option. I will now assume that damage dealt and damage taken are thus a single quantity. Therefore, the trigger for Aura of the Guardian occurs after resistances are applied.
But does the reaction remove its own trigger? Is this a special case?
One thing we do know is that reactions occur after their triggers (from the DMG):
[...] If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes [...]
Except when they don't! There are those strange cases of reactions such as shield and absorb elements, that either involve time-travel or some other odd, not-particularly-well-defined interaction with the rules. We have a lot of question about shield but I'll only link two here:
So we have to asks ourselves "Does Aura of the Guardian's reaction interrupt its trigger or come after its trigger?" Unfortunately, this isn't particularly clear, and it isn't even clear what happens in the cases where we know something does interrupt its trigger so unfortunately even getting the answer might not be helpful in this case.
The feature does not explicitly state that it interrupts its trigger, but I wouldn't say absorb elements and shield do this extremely explicitly either so I would really say that it is going to be up to the GM whether or not the reaction interrupts, cancels, or has some other interaction with its trigger.
Regardless, one key sentence might make none of this matter
The Aura of the Guardian feature contains the following sentence:
[...] this damage can't be reduced in any way [...]
We cannot know how far this statements was meant to apply, or what exactly it meant when saying "this damage". Did it mean only the damage after it transfers, or the entire damage chain even from before the transfer when damage reduction and damage resistance would have applied? This, again, requires a GM's call, though I would rule that it was intended to only affect the damage from after the transfer but that is only my interpretation of the text, nor do I have any especially strong reasoning or evidence for why I would make that decision.
Something else worth considering is what resistance and damage reduction are
These are things that express a specific character's ability to shrug off damage or their natural, well, resistance to something. This is something they benefit from due to their own circumstances, and these circumstances (likely) do not apply to the Paladin as well. However, this doesn't actually get us anywhere since things like warding bond have their damage transfer occur after resistances are applied and wading bond, just like Aura of the Guardian, involves that ever-logic-defying thing: magic.
And so, applying what I would call logic, results in the conclusion that damage reductions and resistances should not apply to damage that is transferred, and yet we have an example where they do. This can, of course be "logic'ed" away as the magic only transferring the actual felt damage, the actual harm dealt and not the actual force of the blow in its entirely, but again, we're in the world of magic and things are fuzzy...
TL;DR: Ask the GM, magic is weird