off-the-books
From Longman Business Dictionaryoff-the-booksˌoff-the-ˈbooks adjective [only before a noun]ACCOUNTING off-the-books payments are those made or received without being officially recorded, so that the tax authorities do not know about themOfficials used to give off-the-books bonuses to senior executives. —off the books adverbThe workers are often paid off the books, well below the minimum wage.