4. When that introduces a relative clause, the clause is usually restrictive; that is, essential to the complete meaning of the sentence because it restricts or specifies the noun or pronoun it modifies. In the sentence The keys that I lost last month have been found, it is clear that keys referred to are a particular set. Without the that clause, the sentence The keys have been found would be vague and probably puzzling. That is used to refer to animate and inanimate nouns and thus can substitute in most uses for who ( m ) and which: Many of the workers that (or who ) built the pyramids died while working. The negotiator made an offer that (or which ) was very attractive to the union. Experienced writers choose among these forms not only on the basis of grammar and the kind of noun referred to but also on the basis of sound of the sentence and their own personal preference.
The relative pronoun that is sometimes omitted. Its omission as a subject is usually considered nonstandard, but the construction is heard occasionally even from educated speakers: A fellow ( that ) lives near here takes people rafting. Most often it is as an object that the relative pronoun is omitted. The omission almost always occurs when the dependent clause begins with a personal pronoun or a proper name: The mechanic ( that ) we take our car to is very competent. The films ( that ) Chaplin made have become classics. The omission of the relative pronoun as in the two preceding examples is standard in all varieties of speech and writing.
13. The conjunction that, which introduces a noun clause, is, like the relative pronoun that, sometimes omitted, often after verbs of thinking, saying, believing, etc.: She said ( that ) they would come in separate cars. He dismissed the idea ( that ) he was being followed. As with the omission of the relative pronoun, the omission of the conjunction almost always occurs when the dependent clause begins with a personal pronoun or with a proper name. This omission of the conjunction that occurs most frequently in informal speech and writing, but it is a stylistic option often chosen in more formal speech and writing.

Did you mean that is?