What to do with metal fascia wrap when attaching ledger board for a pergola?
You should probably leave all weatherproofing in place. The key is to prevent water from draining into unwanted areas, which means that you may want to add flashing to move the drip edge outward and over the ledger. Whether and how you'd do that depends on your pergola design.

You may also opt to simply seal all penetrations through the fascia cover by sandwiching a rubber or foam layer. Moisture will have a tendency to soak into that joint and through nail or screw holes.