There are some papers out there trying to find that out. But all are just
bits and pieces to the puzzle.
https://www.apiservices.biz/documents/articles-en/effect_oxalic_acid_on_varroa_destructor_and_honeybees.pdf

Aside from the footpads there are other effects:
- increased self grooming (likely not the main reason) as only low
percentage of mites had wounds even fewer mortal ones

Most interestingly it's not only direct contact, that kills mites, but also
feeding on mites, that have ingested oxalic acid.

>  The same dose of 70 μg per bee was used when applying oxalic acid orally,
> though the solution was first diluted tenfold to facilitate ingestion by
> the bees and to prevent precocious bee death due to damage to the digestive
> tract caused by too concentrated acid. In this group, mites did die despite
> not coming into outer contact with oxalic acid.
>

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