How do you remove documents that contain a certain property (using $exists) in Mongoose?

I have a query that works fine in Mongo but I'm having problems getting the query to work in Mongoose.

It is when I'm trying to delete documents that contain a particular nested property. Heres the query using stock Mongo.

db.cats.remove({ 'myProp.some.nested': { $exists:true }})

And I've tried the following in Mongoose (just in the node repl using the example from the website).

var mongoose = require('mongoose');

mongoose.connect("mongodb://127.0.0.1:27017/mydb")

var Cat = mongoose.model('Cat', { name: String, myProp:{} });

var kitty = new Cat({ name: 'Zildjian', myProp:{ some:{  nested:'prop' } } });

kitty.save();

Cat.where('myProp.some.nested').exists().remove(console.log)    
> [Error: key myProp.some.nested must not contain '.'] null


Cat.find({'myProp.some.nested':{ $exists:true } }).remove(console.log)
> [Error: key myProp.some.nested must not contain '.'] null


Cat.remove({'myProp.some.nested':{ $exists:true } }).exec(console.log)
> [Error: key myProp.some.nested must not contain '.']

The finder works as expected.

Cat.find({'myProp.some.nested':{ $exists:true } }).exec(console.log)

{ domain: null,
    _events: { err: [Function], complete: [Function] },
    _maxListeners: 10,
        emitted: {},
    ended: false }
> null [ { _id: 53d6e1a8c5828df27ae23091,
    name: 'Zildjian',
    myProp: { some: { nested: 'prop' } },
    __v: 0 } ]