Нашёл решение :)
The object what you pass as a parameter to destroy will eventually end up as the settings parameter to a jQuery.ajax call.
So if you need to send additional data you need to use the data proeprty:
var thisDeal = new WhiteDeals.Models.EditorDeal({ id: dealID });
thisDeal.destroy({data: { program_id: dealProgram.id }, processData: true})
