Have you looked at the query plan?
Did you try to use four-part notation:
INSERT OraLinkedServer.catalog.sch.Pilots(PilotID)
select top 10000 PilotID from Pilots_sqlserver
Personally, I would look for alternatives, Either take the data over a client, or at least use the corresponding to a linked server on the Oracle side. (I assume they have something, but I don't know Oracle.)