What's this off-white particulate stuff on my pickled asparagus?
From luv2garden.com:

Powdery Mildew “appears as a dusty white to gray coating over leaf surfaces or other plant parts. In most cases this fungal growth can be partially removed by rubbing the leaves. It might be identified incorrectly as dust that has accumulated on the leaves.

So it appears to be powdery mildew on your asparagus...
From Ask an Expert:

Soaking leaves in hydrogen peroxide will kill powdery mildew. However, I would not recommend eating leaves with powdery mildew on them. Powdery mildew is not toxic to humans, but fungi cause allergic reactions in some people.

But hold up! Since the asparagus is pickled, powdery mildew just might not be the case.
From reddit:

The flecks are actually a protein buildup called rutin, a natural flavonoid in asparagus that sometimes reacts harmlessly with the vinegar. Rutin is created within pickled asparagus when asparagus is heated within an acid such as vinegar in the pickling process. Through this process, rutin is drawn out of the asparagus.


So the white specks on your asparagus should be rutin.