C# MongoDB:estrae un elemento dalla matrice di un documento nidificato in base a un ID

se ho compreso correttamente la tua esigenza, un pullFilter è quello che ti serve.

var filter = Builders<UserCollection>.Filter.Where(u => u.User.Contacts.Any(c => c._Id == contactID));
var update = Builders<UserCollection>.Update.PullFilter(u => u.User.Contacts, c => c._Id == contactID);
collection.UpdateOne(filter, update);

ecco il programma completo per i test se qualcuno è interessato.

using MongoDB.Entities; // PM> Install-Package MongoDB.Entities
using MongoDB.Bson;    
using System.Linq;

namespace StackOverflow
{
    public class Program
    {
        public class UserCollection : Entity
        {
            public User User { get; set; }
        }

        public class User
        {
            public Contact[] Contacts { get; set; }
        }

        public class Contact
        {
            public ObjectId _Id { get; set; }
        }

        private static void Main(string[] args)
        {
            new DB("test");

            var contactID = ObjectId.GenerateNewId();

            (new UserCollection
            {
                User = new User
                {
                    Contacts = new[]
                    {
                        new Contact { _Id = ObjectId.GenerateNewId()},
                        new Contact { _Id = contactID}
                    }
                }
            }).Save();

            DB.Update<UserCollection>()
              .Match(u => u.User.Contacts.Any(c => c._Id == contactID))
              .Modify(b => b.PullFilter(u => u.User.Contacts, c => c._Id == contactID))
              .Execute();
        }
    }
}