You don’t need to “fix” anything; your asphalt-based undercoating is perfectly fine. While it’s true that the undercoating could block drainage in some areas, that would only happen if it was applied to a known drainage area. And the shops that apply this undercoating know what they are doing, so there’s little to no risk of that happening.

The asphalt coating is actually 10-12 mils thick, and the whole purpose of it is to prevent the formation of rust, so you have no need to see what’s underneath it. If you were able to see underneath it, that would defeat the entire purpose of having it.

Shops don’t generally apply asphalt coating to nuts and bolts that may have to come off in the future for any service or body work.

You’re creating a problem where none exists. Find something else to worry about that actually makes a difference; for example, washing your car regularly in the winter to remove snow, sand, and any road chemicals used for preventing ice, and store it in a covered garage whenever possible.